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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35000
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.29
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.63
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.21
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.88
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  495.85
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.53
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.06
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.14
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.88
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.34
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.48
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4869.94
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907872
   j =  2                              :            46061
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45490
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869490
   j =  1                              :        399909021
   j =  2                              :            45488
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.42
 p-value of test no 115                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.73
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.70
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.12
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.83
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.59
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.74
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.71
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.14
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  171.15
 p-value of test no 141                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17512.14
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.95
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.07
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.55
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.38
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.20
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.81
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.08
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.80
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.88
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.88
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.57
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.51
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.52
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.47
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   43.20
 p-value of test no 165                :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.01
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.87
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.28
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.53
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.14
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.16
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.94
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.13
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.15
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.79
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 193                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.95
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.26
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.67
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.83
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.22
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.42
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.24
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.84
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12085.91
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12133.69
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.69
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999926984
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.26
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000011239
 
 Normal statistic for number of bits   :   0.089
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:00.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35001
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4192
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.16
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.01
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.70
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.23
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.72
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.01
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.77
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.97
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.23
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.31
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.11
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.74
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.17
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908002
   j =  2                              :            45993
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.52
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.65
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.25
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.27
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.03
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 126                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
 p-value of test no 127                :    0.9948
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 128                :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.82
 p-value of test no 129                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.83
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17203.37
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.37
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.90
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.20
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.73
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.70
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.61
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.20
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.16
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.23
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.36
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.19
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.55
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.23
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.53
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.60
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.49
 p-value of test no 165                :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.50
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.56
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.85
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.71
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.62
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.42
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.10
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.47
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.72
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.32
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.59
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.52
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    2.10
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.48
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.01
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.95
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.78
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.20
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.99
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.81
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.71
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.51
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.16
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12264.71
 p-value of test no 230                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.59
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999951929
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.48
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000012646
 
 Normal statistic for number of bits   :   0.100
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:57.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35002
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.80
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.64
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.93
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.23
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.87
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.08
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.05
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.84
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.73
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.30
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.73
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.61
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5013.34
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45350
 p-value of test no 70                 :    0.9933
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869350
   j =  1                              :        399909300
   j =  2                              :            45350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908252
   j =  2                              :            45865
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.73
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.14
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.17
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.01
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.76
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.54
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.48
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.29
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.72
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.40
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.33
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.57
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.36
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.12
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.26
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.44
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.02
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.84
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.07
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.74
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.82
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.24
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.73
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.41
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.50
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.71
 p-value of test no 166                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.16
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.07
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.45
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.64
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.47
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.08
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.28
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.43
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.70
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.14
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.61
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 185                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   43.00
 p-value of test no 199                :  5.7e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 201                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.62
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.20
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.74
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.07
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -5.41e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.79
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.60
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.54
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.82
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.27
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12128.08
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000100171
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.34
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000027721
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:48.32
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  87  LongestHeadRun, r = 27          5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35003
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7539
 p-value of test no 18                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.93
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.23
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.60
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.50
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.47
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.00
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1304.95
 p-value of test no 56                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.34
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.52
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.39
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.35
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.29
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908387
   j =  2                              :            45805
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908488
   j =  2                              :            45750
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
 p-value of test no 101                :    0.9973
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.19
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.54
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.69
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.92
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.92
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.14
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.02
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.87
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.02
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.14
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.20
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.10
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.10
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.53
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.51
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.46
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.00
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.46
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.27
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.51
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.86
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.21
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.05
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.69
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.37
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.10
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.93
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.94
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.99
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.51
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.76
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.83
 p-value of test no 177                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.51
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.87
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.91
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.26
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.40
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.38
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.49
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.33
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.72
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.04
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11558.15
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11522.08
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.16
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999979694
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.09
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000060925
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 240                :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:15.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35004
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7581
 p-value of test no 20                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.95
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.55
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.91
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.17
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   91.72
 p-value of test no 50                 :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.70
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.88
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.41
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.59
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6921.64
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
 p-value of test no 58                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.32
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.79
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.91
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.66
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.71
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908505
   j =  2                              :            45740
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908487
   j =  2                              :            45746
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 98                 :    0.9965
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.61
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.49
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.43
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.29
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.51
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.63
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.02
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.49
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.72
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17173.88
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.96
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.61
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.52
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.58
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.99
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.94
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.89
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.18
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.08
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.82
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.93
 p-value of test no 157                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.11
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.71
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.35
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.98
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.94
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.04
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.81
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.02
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.47
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.21
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.21
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.90
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.68
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.91
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.45
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5233.75
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.46
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.11
 p-value of test no 175                :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.87
 p-value of test no 176                :  5.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.84
 p-value of test no 177                :    0.9978
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.97
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
 p-value of test no 186                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   43.00
 p-value of test no 197                :  5.7e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.99
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.98
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.34
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.74
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.93
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.32
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 224                :  8.7e-4    *****
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5084.78
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.29
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.20
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.21
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.34
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.59
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999824876
 
 Normal statistic for number of bits   :   -1.38
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.74
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000047365
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.055
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:42.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  86  LongestHeadRun, r = 0           5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35005
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.70
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.52
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.50
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.22
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.04
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.34
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.79
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.36
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.33
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.16
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907664
   j =  2                              :            46159
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45571
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869571
   j =  1                              :        399908861
   j =  2                              :            45565
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.53
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.59
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.01
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.26
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.27
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.40
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.60
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.91
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.35
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.76
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 138                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.05
 p-value of test no 141                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.16
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.01
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.16
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.07
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.13
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.10
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.43
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.96
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.55
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.53
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.06
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.63
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.02
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.12
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.85
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.92
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.09
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.25
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.20
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.49
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.82
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.53
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.05
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.91
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.29
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.14
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.24
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.89
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.57
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.01
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.50
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 204                :  4.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 206                :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.82
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 210                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.88
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.21
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.56
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.20
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.82
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.22
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.60
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.05
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.91
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000092266
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.07
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999944231
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:23.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35006
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.26
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.13
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.11
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.31
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.73
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.64
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.67
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.32
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.15
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.67
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.96
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4862.32
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908725
   j =  2                              :            45630
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907709
   j =  2                              :            46141
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.24
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.83
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.74
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.80
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.67
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.28
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.41
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.50
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.79
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 143                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17013.01
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.31
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.54
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.72
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.48
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.69
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.75
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.77
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.29
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.58
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.61
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.00
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.72
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.50
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.16
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.11
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.08
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.42
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.74
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.20
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  460.98
 p-value of test no 171                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.08
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.33
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.55
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.14
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.43
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.41
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.79
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.28
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9776.28
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.47
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.38
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.92
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.43
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.75
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.55
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.21
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999905774
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.49
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000087847
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:27.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35007
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5330
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.32
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.54
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.14
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.34
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.19
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.49
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.82
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.29
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.91
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.34
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.76
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.23
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.15
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.94
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46069
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870069
   j =  1                              :        399907865
   j =  2                              :            46063
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907799
   j =  2                              :            46093
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9942
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.20
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.35
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.11
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.02
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.44
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.94
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.95
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.39
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.00
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.57
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.52
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.22
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.81
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.59
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.27
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.98
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.52
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.02
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.89
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.06
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.01
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.00
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.91
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.50
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.76
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.58
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.10
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.99
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.60
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.79
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.66
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.79
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.24
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.45
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 185                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 186                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    5.83
 p-value of test no 187                :  1.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.31
 p-value of test no 188                :  4.7e-4    *****
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.11
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.51
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.45
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.86
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.78
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.67
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.93
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.31
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.43
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.44
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.18
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.24
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999862628
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.57
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000149581
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:29.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35008
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997271
   j =  2                              :             1363
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    5.54
 p-value of test no 39                 :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9938
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.98
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.21
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.84
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.26
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.23
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.68
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.33
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.12
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.68
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.81
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.42
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.38
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4951.48
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908924
   j =  2                              :            45535
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908096
   j =  2                              :            45946
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 87                 :  3.9e-3
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.40
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.77
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.92
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.03
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.38
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.23
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.08
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.67
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.68
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.43
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.43
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.76
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.33
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.19
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.72
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.90
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.51
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.02
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.50
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.07
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.96
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.64
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.67
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.06
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.99
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4779.35
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.35
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.23
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.16
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.92
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.47
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.24
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.88
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.12
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.83
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.90
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.40
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.85
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.18
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.20
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.41
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.15
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.16
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.59
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.54
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999910340
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.80
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000024670
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:06.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35009
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7574
 p-value of test no 15                 :  1.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.06
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9914
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.78
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.49
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.21
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.44
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.49
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.05
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7001.60
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.53
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.43
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.85
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.53
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4935.62
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907764
   j =  2                              :            46112
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908008
   j =  2                              :            45990
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.86
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.37
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.64
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.88
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.44
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.61
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.60
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.44
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17630.93
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.16
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.65
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.74
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.90
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.03
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.10
 p-value of test no 151                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.03
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.80
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.09
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.49
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.27
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.57
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.35
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.97
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.15
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.32
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.73
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.72
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.00
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.84
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.97
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  448.37
 p-value of test no 169                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.81
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.41
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.14
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.84
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.62
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.82
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.35
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.39
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.15
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 205                :    0.9941
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.82
 p-value of test no 207                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.43
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.68
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.25
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.07
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.06
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.78
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.97
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11453.78
 p-value of test no 230                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999988862
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.62
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000004972
 
 Normal statistic for number of bits   :   0.039
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 252                :    0.9972
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35010
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 11                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.79
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.03
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.75
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.36
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.14
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.96
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7151.25
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.64
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.18
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.64
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.43
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908714
   j =  2                              :            45631
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908666
   j =  2                              :            45664
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.15e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.44
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.39
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.94
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.77
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.02
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.57
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.98
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.08
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.83
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.28
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.64
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.29
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.39
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.32
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.83
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.92
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.96
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.21
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.81
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.77
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.62
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.11
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.12
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.13
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.05
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.05
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.18
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.33
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.58
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.55
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.64
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.48
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.75
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.34
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.98
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    2.28
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.41
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.22
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.96
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.54
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.58
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.73
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.47
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.04
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.80
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.47
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.22
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000081814
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.21
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999805133
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.031
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:36.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35011
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.06
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.31
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.40
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.51
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.02
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.23
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.41
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.10
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.14
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.85
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.34
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.45
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.14
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907882
   j =  2                              :            46056
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908166
   j =  2                              :            45908
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 83                 :    0.9930
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.53
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.14
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.59
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.60
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.48
 p-value of test no 123                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.07
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.84
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.81
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.90
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.84
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.38
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17355.92
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.94
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.48
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.32
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.16
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   69.69
 p-value of test no 151                :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.96
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.06
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.17
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.20
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.93
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.39
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.82
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.88
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.32
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.52
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.26
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.73
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.94
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.93
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.49
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.82
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.70
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.21
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.06
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.35
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.51
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.49
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.70
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.29
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.16
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 193                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 201                :  1.2e-3
 
 Anderson-Darling statistic = A2       :    6.10
 p-value of test no 202                :  9.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  274.01
 p-value of test no 203                :  4.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.07
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.64
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.05
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.64
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.19
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.56
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.93
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.82
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.41
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.10
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000055324
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.71
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999942710
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:44:15.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 H (L=50, r=25)      6.4e-4
  88  PeriodsInStrings, r = 0         4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35012
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.76
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.01
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.95
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.00
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.33
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7205.72
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.07
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.12
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.52
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.52
 p-value of test no 67                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.72
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46547
 p-value of test no 70                 :  9.4e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870547
   j =  1                              :        399906908
   j =  2                              :            46543
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908320
   j =  2                              :            45837
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.28
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.10
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.62
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.32
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.95
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.42
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.13
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17271.33
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.61
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.08
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.34
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.68
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.52
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.75
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.30
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.49
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.91
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.02
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.48
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.97
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.83
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.38
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.23
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.10
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.04
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.79
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.95
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.45
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.84
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.50
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.56
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.63
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.31
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.05
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.80
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.82
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.08
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-3
 p-value of test no 185                :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.71
 p-value of test no 188                :  3.3e-3
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.41
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.69
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.58
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.82
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.18
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.46
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.51
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.26
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.87
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.53
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.83
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.94
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.77
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999889502
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.49
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999964145
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:23.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  44  CollisionPermut, r = 0          9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35013
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1222
 p-value of test no 11                 : 1 -  4.8e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334342
   j =  1                              :        599997556
   j =  2                              :             1222
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.20
 p-value of test no 46                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.69
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.11
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.52
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.02
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.19
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.98
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.48
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6841.91
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.44
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.85
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.29
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.58
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908818
   j =  2                              :            45582
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908650
   j =  2                              :            45672
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.88
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.65
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.29
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.01
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.38
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.96
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.94
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.62
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.51
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17308.20
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.96
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.23
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.78
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.62
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.04
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.39
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.18
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.91
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.46
 p-value of test no 154                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.27
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.01
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.42
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.71
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.79
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.34
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.46
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.81
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.74
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.67
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.68
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.89
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.58
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.26
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.71
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.51
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.04
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.34
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.22
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.38
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.46
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.16
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.57
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.25
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.57
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.70
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.96
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.60
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.45
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.20
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.05
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.54
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999973268
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.06
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000061057
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:31.75
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  4.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35014
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7092
 p-value of test no 15                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    3.03
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     261
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.61
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.45
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.75
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.25
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.24
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.25
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7080.15
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.35
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.43
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.82
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.54
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.29
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908638
   j =  2                              :            45672
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.77
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.14
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.60
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.42
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.38
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.62
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.53
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.82
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.61
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.22
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.44
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.33
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.74
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.86
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.34
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.73
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.09
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.18
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.35
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.45
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.76
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.81
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.83
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.62
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.19
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.65
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.39
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.77
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.57
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.39
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.18
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.45
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.76
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.84
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.39
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.27
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.98
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.74
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.34
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.62
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.30
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.56
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.14
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.06
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.11
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.67
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999927140
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.14
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000104659
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:59.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35015
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 11                 :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.33
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.87
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.75
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.30
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.83
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.65
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.94
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.38
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.85
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.17
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.22
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.43
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.06
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.49
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908306
   j =  2                              :            45838
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907828
   j =  2                              :            46080
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.21
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.09
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.00
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.32
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.26
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.71
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.19
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.50
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.83
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.75
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.72
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.94
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.60
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.45
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.55
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.09
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.69
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.08
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.45
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.54
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.22
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.79
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.39
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.60
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.00
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.70
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.23
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.41
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.14
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.58
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.11
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.04
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.58
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.72
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.62
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.69
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.11
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.36
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.43
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.23
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.87
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.74
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.91
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.42
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.49
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.87
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.40
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.37
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.14
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999975476
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.01
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000126139
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:37.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35016
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4199
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.24
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.18
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.44
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.67
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.45
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.49
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.18
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.46
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.15
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.38
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.69
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.25
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.91
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908801
   j =  2                              :            45598
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907931
   j =  2                              :            46033
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 101                :    0.9921
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.69
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.52
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.74
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.35
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.59
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.98
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.75
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.51
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.20
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.80
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.20
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.86
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.72
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.49
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.03
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.55
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.10
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.08
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.75
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.06
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.81
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.93
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.54
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.43
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.54
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.94
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.02
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.60
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.06
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.77
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.29
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.09
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.31
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.53
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.31
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.10
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.45
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.60
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.13
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.88
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.73
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.66
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9748.62
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.39
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.48
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.12
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.01
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.05
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.06
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.03
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000108424
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.62
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000077710
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-3
 p-value of test no 236                :    0.9985
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 237                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.05
 p-value of test no 238                :    0.9988
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 245                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:33.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35017
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 27                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.02
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.17
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.04
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.50
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.47
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.47
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  371.93
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.96
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.32
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.36
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.59
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.47
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.50
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.35
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908061
   j =  2                              :            45965
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45643
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869643
   j =  1                              :        399908721
   j =  2                              :            45629
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.87
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.08
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.20
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.66
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.47
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.34
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 132                :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.68
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.86
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17325.45
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.98
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.00
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.87
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.11
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.57
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.42
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.45
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.52
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.34
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.16
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.87
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.74
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.69
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.11
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.59
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.25
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.99
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.47
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.42
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.96
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.26
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.40
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.87
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.82
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.11
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.12
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.21
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.29
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.26
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.57
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4662.81
 p-value of test no 222                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.95
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.35
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.91
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.03
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.32
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.78
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000037807
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.78
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000126673
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.45
 p-value of test no 243                :    0.9929
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-4
 p-value of test no 250                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.66
 p-value of test no 253                :  3.9e-3
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:50.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35018
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7130
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.08
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.78
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.09
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.46
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.70
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.77
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.95
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.98
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.15
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.36
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.01
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.03
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.11
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45561
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869561
   j =  1                              :        399908882
   j =  2                              :            45553
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45535
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869535
   j =  1                              :        399908933
   j =  2                              :            45529
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 100                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.60
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.36
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.08
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.75
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.18
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.78
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.10
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.44
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.80
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.85
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.58
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.71
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.85
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.26
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.29
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.59
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.64
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.92
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.10
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.71
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.99
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.31
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.32
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.76
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.59
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4784.65
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.73
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.63
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.96
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.79
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.17
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.32
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.32
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.93
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.96
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.54
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.72
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.10
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.14
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5137.23
 p-value of test no 226                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.88
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.02
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.90
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.27
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.75
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999986159
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.73
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000038863
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    2.00
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:52.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35019
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 11                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 20                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.67
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.75
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.82
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.49
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.89
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  495.79
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.88
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.27
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.98
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.17
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.14
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.84
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907735
   j =  2                              :            46128
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908005
   j =  2                              :            45990
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-4
 p-value of test no 113                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.35
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.66
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.96
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.37
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.88
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.37
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.99
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.96
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.61
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.46
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.70
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.16
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.20
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.33
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.21
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.59
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.47
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.82
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.29
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.39
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.33
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.74
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.58
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.37
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.08
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.09
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.87
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.31
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.81
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.76
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.64
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.20
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.46
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4777.86
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  318.03
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.58
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.26
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 185                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.91
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.82
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.87
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.67
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.27
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.96
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.74
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.81
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.05
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.24
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.60
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.03
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000034522
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.59
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999899342
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:05.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35020
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 11                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    5.48
 p-value of test no 44                 :  1.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.85
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.92
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.36
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.09
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.18
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.06
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.16
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.40
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.85
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.31
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.66
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.88
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.09
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.64
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.45
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908467
   j =  2                              :            45765
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9917
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.40
 p-value of test no 115                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.85
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.21
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.45
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.37
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.51
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.80
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.90
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.64
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17604.36
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.98
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.94
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.05
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.50
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.50
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.86
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.19
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.80
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.21
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.69
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.51
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.33
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.33
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.15
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.13
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.45
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.10
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.43
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.96
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.01
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.58
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.28
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.73
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.07
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.97
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.18
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.07
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.69
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.73
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.04
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.42
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.65
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.39
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.87
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.28
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.74
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.88
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.85
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000245956
 
 Normal statistic for number of bits   :    1.94
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.82
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000034099
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 236                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 237                :  5.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.40
 p-value of test no 238                :  8.2e-3
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:08.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35021
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.87
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.86
 p-value of test no 48                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.84
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.32
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.84
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.40
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.08
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.39
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.64
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.73
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.70
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.48
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.84
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.82
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908407
   j =  2                              :            45789
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908420
   j =  2                              :            45784
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 84                 :    0.9952
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.60
 p-value of test no 116                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.34
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.29
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.99
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.19
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.79
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.34
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.66
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.39
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.24
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.29
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.10
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.55
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.17
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.86
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.15
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.37
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.49
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.72
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.90
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.93
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.83
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.71
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.31
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.25
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.37
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.89
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.76
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.21
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.59
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.35
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.80
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.81
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.69
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.23
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.18
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.76
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.72
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.80
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.57
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.02
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.57
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.50
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.14
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.04
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11568.82
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11745.94
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.82
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000128902
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.66
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999958568
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35022
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.26
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.64
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.19
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.57
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.43
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.09
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.92
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1356.98
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.03
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.57
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.27
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.05
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.49
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.16
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46297
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870297
   j =  1                              :        399907409
   j =  2                              :            46291
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908450
   j =  2                              :            45766
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 1.63e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.80
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.22
 p-value of test no 120                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.67
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.15
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.32
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.94
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.85
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.92
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17595.46
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.79
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.27
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.08
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.76
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.98
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.60
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.36
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.57
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.16
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.63
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.18
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.07
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.05
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.61
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.97
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.69
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.96
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.55
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.75
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.46
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.45
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.41
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.64
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.80
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.16
 p-value of test no 184                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.53
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.29
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.92
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.78
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.13
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.22
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.35
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.20
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.17
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.35
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.09
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.38
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999995309
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.92
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000240388
 
 Normal statistic for number of bits   :    1.90
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35023
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.43
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.05
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.05
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.26
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.18
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.62
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.53
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7268.24
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.96
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.57
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.75
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4904.11
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907811
   j =  2                              :            46093
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46116
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870116
   j =  1                              :        399907771
   j =  2                              :            46110
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.025
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.74
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.40
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.05
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.29
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.42
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.11
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.86
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17368.49
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.50
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.51
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.11
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.53
 p-value of test no 149                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.07
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.47
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.13
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.99
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.07
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.45
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.69
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.37
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.20
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.26
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.59
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.70
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.07
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.27
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.38
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.91
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.26
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.21
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.81
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.35
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.60
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.60
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.24
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.65
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.81
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.04
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.13
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.71
 p-value of test no 216                :  1.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.02
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.35
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.52
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.10
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.47
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.55
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.99
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999863273
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.88
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999925394
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.095
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:24.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  92  HammingCorr, L = 30             1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35024
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.74
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.31
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.61
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.95
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.82
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.15
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.50
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.37
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7255.09
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.09
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.56
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.99
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.45
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.88
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908400
   j =  2                              :            45791
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908329
   j =  2                              :            45834
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 115                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.29
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.26
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.86
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.32
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.67
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.68
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.38
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.78
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17593.54
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.19
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.57
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.82
 p-value of test no 148                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.69
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.44
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.67
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.58
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.02
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.93
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.69
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.54
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.08
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  204.58
 p-value of test no 162                :  9.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.20
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.91
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.36
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.24
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.37
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.52
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.68
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.85
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.13
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.63
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.17
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.49
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.84
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.71e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.84
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.94
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.96
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 208                :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9715.04
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10329.85
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.97
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.88
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.14
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.94
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.55
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.93
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.82
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000093358
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.79
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999915488
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 M (L=1000, r=20)    9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35025
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7543
 p-value of test no 19                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.16
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.88
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.63
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.26
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1306.47
 p-value of test no 56                 :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.43
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.71
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.23
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.23
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.37
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.70
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.91
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.18
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.35
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.65
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.73
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 132                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   67.74
 p-value of test no 133                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 137                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.77
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17254.43
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.42
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.22
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.29
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.60
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.53
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.76
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.14
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.29
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.89
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.98
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.86
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.16
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.62
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.38
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.88
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.41
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.06
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.96
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.02
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.55
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.70
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.04
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.37
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.87
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.17
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.77
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.49
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.71
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.42
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.17
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.91
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.76
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4658.82
 p-value of test no 226                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.66
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.96
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11501.67
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.02
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.83
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999923861
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.36
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000058756
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    2.39
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:52.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35026
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.70
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.49
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.66
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.42
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.18
 p-value of test no 52                 :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.68
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.24
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.59
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.30
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.13
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.50
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
 p-value of test no 62                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.70
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.56
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4877.77
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45580
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869580
   j =  1                              :        399908845
   j =  2                              :            45570
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908043
   j =  2                              :            45974
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.83
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.81
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.32
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.61
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.90
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17091.18
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.20
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.77
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.05
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.68
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.74
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.24
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.48
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.34
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.89
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.09
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.90
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.48
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.84
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.56
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.95
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.61
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.48
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.77
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.60
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.01
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.89
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.56
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.52
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.37
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.97
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.37
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.01
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.75
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.75
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.78
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.08
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.79
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.86
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.14
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.44
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-3
 p-value of test no 208                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 210                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10432.68
 p-value of test no 211                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.53
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4695.65
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4704.91
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.79
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.65
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.09
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.94
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.29
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999886139
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.63
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000048193
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:04.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35027
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     540
 p-value of test no 31                 :    0.9931
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.78
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.10
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.69
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.91
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.09
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.51
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.61
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.92
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6755.96
 p-value of test no 57                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.65
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.11
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.85
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.07
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.82
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907924
   j =  2                              :            46035
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45508
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869508
   j =  1                              :        399908991
   j =  2                              :            45494
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 81                 :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  7.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.82
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.39
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.50
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.35
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.19
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.79
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.61
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.05
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.36
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.72
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.47
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.46
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.10
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.83
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.91
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.38
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.44
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.30
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.29
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.58
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   41.94
 p-value of test no 160                :    0.9990    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.89
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.96
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.88
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.68
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.75
 p-value of test no 165                :  9.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.88
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.56
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.94
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.67
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.96
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.02
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.07
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.18
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.83
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.70
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.17
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.87
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.79
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.86
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.22
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.74
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
 p-value of test no 220                :    0.9955
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.94
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.21
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.69
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.69
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.37
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11464.49
 p-value of test no 230                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.46
 p-value of test no 231                :    0.9911
 
 
 -----------------------------------------------
 Total number of bits:  8000015757
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.42
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999928658
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:55.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 C (L=1000, r=0)     0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35028
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 27                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.72
 p-value of test no 47                 :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.13
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.29
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.92
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.56
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.81
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.13
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.21
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.32
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.78
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.20
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.29
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.07
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46433
 p-value of test no 70                 :  5.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870433
   j =  1                              :        399907137
   j =  2                              :            46427
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907919
   j =  2                              :            46036
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 79                 :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9910
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.38
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.83
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.11
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.91
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.53
 p-value of test no 124                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.10
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.88
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.19
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.18
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 144                :  8.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16929.79
 p-value of test no 145                :    0.9965
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.61
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.08
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.56
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.25
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.08
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.91
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.29
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.65
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.36
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.09
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.92
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.57
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.93
 p-value of test no 161                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.76
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.66
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.36
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.86
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.26
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.03
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.00
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.53
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.26
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.95
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.33
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.92
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.93
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.30
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.85
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.84
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.62
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.39
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.15
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.77
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.33
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.00
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.88
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.64
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.75
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.11
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.68
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000050545
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.21
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000013969
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.63
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:25.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35029
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 4                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7517
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.73
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.49
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.91
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.49
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.82
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.64
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.36
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7302.15
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.07
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.43
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.26
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.88
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907925
   j =  2                              :            46024
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907757
   j =  2                              :            46120
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.15
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.19
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.14
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.62
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.96
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.66
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.68
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.94
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17400.47
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.55
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.89
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.31
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.57
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.88
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.10
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.05
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.13
 p-value of test no 154                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.65
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.65
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.70
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.43
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.60
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.33
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.44
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.53
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.17
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.93
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.13
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.16
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.25
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.15
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.70
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.40
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.06
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.18
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.02
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.27
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.90
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.37
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.14
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.44
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.82
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.42
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.86
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.63
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.73
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.72
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 223                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5095.77
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.65
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.88
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.59
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.88
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.93
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999989204
 
 Normal statistic for number of bits   :  -0.085
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.16
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999996548
 
 Normal statistic for number of bits   :  -0.027
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:42.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35030
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.72
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.18
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.08
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.41
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.42
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.61
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.84
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.14
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.80
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.05
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.90
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.96
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.83
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908042
   j =  2                              :            45979
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908471
   j =  2                              :            45760
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.41
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.43
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.87
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.99
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.61
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.35
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.62
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.33
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.46
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.66
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.39
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.83
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.13
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.27
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.81
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.80
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.38
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.45
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.42
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.46
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.38
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.02
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.36
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.35
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.43
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.43
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.50
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.05
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.61
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.06
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.41
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.04
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.16
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.05
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.60
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.72
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.86
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.00
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.73
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.91
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.49
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.41
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.26
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.59
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.54
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.33
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.04
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11954.67
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.64
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.24
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000048976
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.90
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999934415
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:19.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35031
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5551
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.08
 p-value of test no 47                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.14
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.51
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.06
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.02
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.47
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  504.76
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.61
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.03
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.58
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.12
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.72
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.60
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5215.54
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908068
   j =  2                              :            45963
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45440
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869440
   j =  1                              :        399909127
   j =  2                              :            45426
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 86                 :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.69
 p-value of test no 115                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  105.57
 p-value of test no 119                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.04
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.69
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.38
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.72
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.05
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.19
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.71
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17326.17
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.68
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.55
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.50
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.06
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.86
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.97
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.40
 p-value of test no 156                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.14
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.16
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.33
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.74
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.59
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.38
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.23
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.62
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.02
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.43
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.26
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.68
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.43
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.61
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.56
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.11
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.60
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.09
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.96
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.93
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.00
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.44
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.70
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.48
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.86
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.09
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4274.56
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.98
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.28
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.17
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.54
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000013939
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.35
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000100066
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:32.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35032
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 27                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    3.07
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.89
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.57
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.72
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.42
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.87
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.29
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.38
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.87
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.72
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.63
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.27
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.77
 p-value of test no 67                 :    0.9906
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4817.95
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908002
   j =  2                              :            45993
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46594
 p-value of test no 71                 :  4.4e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870594
   j =  1                              :        399906815
   j =  2                              :            46588
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 78                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.46
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.78
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.81
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.75
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.29
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.78
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.70
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.42
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.68
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.85
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16956.63
 p-value of test no 145                :    0.9947
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.41
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.98
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.84
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.76
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.95
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.48
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.00
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.70
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.95
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.46
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.02
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.19
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.38
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.50
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.64
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.70
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.05
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.20
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.60
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.83
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.90
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.97
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.00
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.86
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.88
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.35
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.51
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.80
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9906
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.35
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 205                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.05
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.35
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.46
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.08
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.83
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.42
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.38
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11554.29
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.26
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.27
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000031960
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.43
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999856772
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:39.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35033
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.23
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.62
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.50
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.57
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.56
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.65
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.61
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.41
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.26
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.94
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.74
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.58
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.42
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908579
   j =  2                              :            45706
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907709
   j =  2                              :            46144
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
 p-value of test no 94                 :    0.9935
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.92
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.45
 p-value of test no 121                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.31
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.87
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.61
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.14
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.48
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.73
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.02
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.69
 p-value of test no 137                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.29
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.24
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.31
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.33
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.89
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.42
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.30
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.19
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.75
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.45
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.48
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.52
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.98
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.52
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.76
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.71
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.55
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.72
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.68
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.03
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.69
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.79
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.93
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.54
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.63
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.41
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.91
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.02
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.46
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.16
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.19
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.36
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.86
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.37
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.68
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.13
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.81
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.16
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.28
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.02
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.30
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999884357
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.80
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000081016
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:59.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35034
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1485
 p-value of test no 10                 :  6.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334605
   j =  1                              :        599997030
   j =  2                              :             1485
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1242
 p-value of test no 11                 :    0.9996    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334362
   j =  1                              :        599997516
   j =  2                              :             1242
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997343
   j =  2                              :             1327
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9931
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9929
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    4.61
 p-value of test no 44                 :  4.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.91
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.75
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.76
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.00
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.64
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.17
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.25
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.42
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.02
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.15
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.33
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45617
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869617
   j =  1                              :        399908770
   j =  2                              :            45609
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908425
   j =  2                              :            45783
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.94
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.14
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.50
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.77
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.31
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.95
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.64
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.78
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.24
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.66
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.00
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.89
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.00
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.54
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.16
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.99
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.10
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.75
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.96
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.99
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.79
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.53
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.01
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.50
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.16
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.31
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.05
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.87
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.50
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.67
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.51
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.37
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.54
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.71
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.91
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.24
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.95
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.70
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.96
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.81
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.02
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.79
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.63
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.74
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.59
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999892943
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000000964
 
 Normal statistic for number of bits   : 7.62e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 250                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 253                :    0.9916
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:15.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           6.5e-4
  11  CollisionOver, t = 21           0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35035
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.76
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.23
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.85
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.13
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.40
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.13
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.30
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.97
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.24
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.45
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.21
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5295.15
 p-value of test no 68                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908008
   j =  2                              :            45993
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45701
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869701
   j =  1                              :        399908601
   j =  2                              :            45695
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.67
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.69
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.56
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.13
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.76
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.19
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.65
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.88
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.63
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.82
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.17
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.59
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.62
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.85
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.19
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.52
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.06
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.55
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.51
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.84
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.59
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.05
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.61
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.74
 p-value of test no 162                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.35
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.18
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.94
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.98
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.44
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.71
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.08
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.93
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.06
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.17
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.89
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.63
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.29
 p-value of test no 196                :  3.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.50
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.59
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.45
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9812.20
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.87
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.40
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.75
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.22
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.31
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.01
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.31
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.46
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999924053
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.24
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999875087
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:16.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35036
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.15
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.50
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.70
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.91
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.57
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.32
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.05
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.51
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.05
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.30
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.25
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907737
   j =  2                              :            46124
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46111
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870111
   j =  1                              :        399907781
   j =  2                              :            46105
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.23
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.33
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.23
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.56
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.01
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.97
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.22
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.53
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17434.52
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.70
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.69
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.65
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.48
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.84
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.15
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.48
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.97
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.87
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.07
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.55
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.50
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.30
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.43
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.21
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.09
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.56
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.87
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.98
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.36
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.62
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.74
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5232.48
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.80
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.12
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.06
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.93
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.15
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.82
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.47
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.22
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.42
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.96
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.43
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.34
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.37
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.20
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.89
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000071380
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.11
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000123538
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:47.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35037
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 12                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.19
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.34
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.73
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.79
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.41
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.73
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.03
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.17
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.58
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7134.81
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.42
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.56
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.69
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.95
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907988
   j =  2                              :            46003
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45563
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869563
   j =  1                              :        399908876
   j =  2                              :            45559
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-5
 p-value of test no 109                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
 p-value of test no 110                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.76
 p-value of test no 111                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.22
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.52
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.76
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.61
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.75
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.60
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17631.03
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.17
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.89
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.52
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.09
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.41
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.34
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.59
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.71
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.83
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.67
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.71
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.11
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.58
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.84
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.42
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.88
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.87
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.93
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.67
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.06
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.92
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.01
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.08
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.59
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.38
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.30
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.73
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.85
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.44
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.57
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.40
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.79
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.55
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.01
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.07
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.54
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.42
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.85
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.13
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.51
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000028141
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.40
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000126316
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:14.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35038
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1502
 p-value of test no 12                 :  1.3e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334622
   j =  1                              :        599996996
   j =  2                              :             1502
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     830
 p-value of test no 25                 :    0.9904
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.04
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.23
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.55
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.29
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.37
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.49
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.26
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.06
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.07
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.71
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.55
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.91
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4904.35
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908648
   j =  2                              :            45670
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45694
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908613
   j =  2                              :            45692
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 92                 :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.22
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.63
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.31
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.30
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.79
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.02
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.77
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.84
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.09
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.46
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.51
 p-value of test no 146                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.98
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.78
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.57
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.14
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.62
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.07
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.17
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.38
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.89
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.33
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.17
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.85
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.70
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.79
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.77
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.02
 p-value of test no 164                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.45
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.01
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.74
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5243.68
 p-value of test no 168                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.70
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.06
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.50
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  468.08
 p-value of test no 172                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.00
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.76
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.78
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.72
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.97
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.23
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.48
 p-value of test no 203                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.99
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10301.62
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.52
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.50
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.51
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.81
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.78
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.07
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.20
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.46
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000108679
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.70
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000163414
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.59
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:53.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           1.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35039
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9950
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.00
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.99
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.73
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.28
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.77
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.36
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.48
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.90
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.52
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.21
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.86
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.17
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46255
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870255
   j =  1                              :        399907492
   j =  2                              :            46251
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908324
   j =  2                              :            45832
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 90                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 92                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.32
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.03
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.06
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.74
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.45
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.05
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.29
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.40
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.85
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.57
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.66
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.48
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.97
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.70
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.81
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.16
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.64
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.44
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.07
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.14
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.71
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.80
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.43
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.80
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.58
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.21
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.17
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.65
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.19
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.70
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.16
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.25
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.64
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.92
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.43
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.44
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.72
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.69
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.82
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    5.85
 p-value of test no 210                :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9556.58
 p-value of test no 211                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.15
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.54
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.65
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3858.27
 p-value of test no 227                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.45
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.50
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.67
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.03
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999997937
 
 Normal statistic for number of bits   :  -0.016
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.81
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000222262
 
 Normal statistic for number of bits   :    1.76
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:40.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  90  HammingWeight2, r = 0           0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35040
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.60
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.79
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.43
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.75
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.87
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.91
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1331.89
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.84
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.75
 p-value of test no 58                 :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 60                 :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.14
 p-value of test no 61                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.45
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.75
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.78
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.92
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.03
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.83
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.86
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.12
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.21
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.50
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 126                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.41
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.74
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.65
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.23
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.44
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.02
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.97
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.12
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.41
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.56
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.98
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.04
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.06
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.43
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.50
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.78
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.44
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.54
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.07
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.44
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.32
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.70
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.05
 p-value of test no 172                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.21
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.36
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.22
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.86
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.77
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.57
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.91
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.53
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.91
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.62
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3859.90
 p-value of test no 228                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.63
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.46
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.17
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999958916
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.18
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999961658
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:00.82
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35041
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.52
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     992
 p-value of test no 25                 :  1.3e-3
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.73
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   25.50
 p-value of test no 46                 :  6.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.51
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.20
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.85
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.52
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.06
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.70
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.17
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.23
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.22
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.83
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.77
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.85
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908686
   j =  2                              :            45654
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908745
   j =  2                              :            45620
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.89
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.70
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.02
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.39
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.12
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.84
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.83
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.28
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.43
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.24
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.91
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17255.88
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.95
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.04
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.44
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.97
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.52
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.50
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.03
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.86
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.03
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.14
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.91
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.31
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.62
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.16
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.42
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.19
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.61
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.02
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.49
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.10
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.41
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.13
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.86
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.63
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.28
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.14
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.63
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.87
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.43
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.24
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9639.03
 p-value of test no 211                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.63
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.63
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.21
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.87
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.48
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.62
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.29
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.04
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000039043
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.33
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000084001
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:19.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  26  SimpPoker, r = 0                6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35042
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    3.48
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.71
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.89
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.07
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.31
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.53
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.00
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.28
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.74
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.75
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.45
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.69
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.02
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.62
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.53
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907799
   j =  2                              :            46096
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907782
   j =  2                              :            46100
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
 p-value of test no 97                 :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.43
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  105.22
 p-value of test no 121                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.68
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.60
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.95
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.33
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.59
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.87
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.53
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17140.42
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.91
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.08
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.96
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.41
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.69
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.28
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.80
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.04
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.22
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.78
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.79
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.06
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.48
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.07
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.19
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.63
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.81
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.99
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.13
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.44
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.02
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.49
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.80
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.67
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.21
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.52
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.80
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.30
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.63
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5083.19
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.86
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.90
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.58
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.14
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.12
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999960716
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.94
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000038296
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:21.67
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35043
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 11                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5332
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.10
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.70
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.67
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.18
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.93
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.35
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.43
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.17
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.71
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.48
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.61
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.75
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.12
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.99
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46104
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870104
   j =  1                              :        399907795
   j =  2                              :            46098
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908612
   j =  2                              :            45691
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-3
 p-value of test no 101                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.27e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.22
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.41
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.09
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.70
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.71
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.31
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.87
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.31
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.73
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.90
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.39
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.33
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.37
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.17
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.01
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.76
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.85
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.94
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.73
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.95
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.17
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.72
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.22
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.05
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.97
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.74
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.11
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.90
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.84
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.19
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.14
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.79
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.37
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.70
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.72
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.39
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.26
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.36
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.71
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.28
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.50
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.13
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.09
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.13
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.56
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.45
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.15
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000104530
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.98
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999910871
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35044
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 10                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    3.22
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.55
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.61
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.85
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.60
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.92
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.68
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7185.15
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.20
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.98
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.97
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5080.68
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908114
   j =  2                              :            45940
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45862
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869862
   j =  1                              :        399908281
   j =  2                              :            45852
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.09
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.30
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.99
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.84
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.52
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.05
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.96
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.97
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.67
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.03
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17732.24
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.10
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.44
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.74
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.53
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.71
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.22
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.13
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.29
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.60
 p-value of test no 155                :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.94
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.53
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  189.87
 p-value of test no 159                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.97
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.35
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.34
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.22
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.94
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.06
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.86
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.68
 p-value of test no 169                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.77
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.85
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.99
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.51
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.90
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.23
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.33
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.82
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.36
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.80
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 204                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 206                :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.49
 p-value of test no 207                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.98
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.79
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.88
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.92
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.70
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.52
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.15
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.03
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.69
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999955235
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.39
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000016627
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:35.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35045
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7513
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.20
 p-value of test no 22                 :  7.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     350
 p-value of test no 37                 :  2.6e-3
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.97
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.24
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.12
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.00
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.26
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.31
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.53
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.17
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.24
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5031.78
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908081
   j =  2                              :            45958
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908020
   j =  2                              :            45984
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -5.94e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.71
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.56
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.83
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.06
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.43
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.27
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.65
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.36
 p-value of test no 134                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.48
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17394.97
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.78
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.14
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.41
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.74
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.01
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.12
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.90
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.59
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.65
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.91
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.30
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.22
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.21
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.27
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.92
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.24
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.83
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.15
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.26
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.76
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.44
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.36
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.55
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.74
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.83
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.39
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.69
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.15
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.14
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.14
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.49
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.53
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.90
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.61
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.83
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.59
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12122.71
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11726.35
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.65
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999984353
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999897767
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:27.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35046
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.26
 p-value of test no 47                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.79
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.06
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.39
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.89
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.31
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7289.86
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.46
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.50
 p-value of test no 65                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.45
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.73
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908572
   j =  2                              :            45708
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908246
   j =  2                              :            45871
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.05
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.31
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.96
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.44
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.92
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.64
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.71
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.17
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.05
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.64
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.27
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.43
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.50
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.27
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.52
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.62
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.55
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.79
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.30
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.85
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.90
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.89
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.32
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.71
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.40
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  588.80
 p-value of test no 163                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.77
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.22
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.14
 p-value of test no 166                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.07
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.00
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.59
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.14
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.37
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5173.26
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.32
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.03
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.63
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.30
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.51
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.13
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.72
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.33
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.83
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.82
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.68
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.73
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.93
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.64
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.73
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.08
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999904394
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.91
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999850814
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:01.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35047
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7104
 p-value of test no 15                 :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.44
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     540
 p-value of test no 31                 :    0.9931
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    3.04
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.64
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.27
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.81
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.36
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.53
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7127.29
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.86
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.46
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.76
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.33
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5174.83
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907978
   j =  2                              :            46008
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908071
   j =  2                              :            45954
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 74                 :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  2.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.31
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.33
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.66
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.50
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.96
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.63
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.03
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.96
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 132                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.30
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.90
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.48
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.47
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.75
 p-value of test no 149                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.71
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.07
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.91
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.98
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.17
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.53
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.99
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.96
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.45
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.03
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.27
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.16
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.08
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.55
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.23
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.83
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.14
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.92
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.46
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.81
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.77
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.50
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.21
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.81
 p-value of test no 176                :  3.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.70
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.76
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.72
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.63
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.00
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.39
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.17
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.80
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.75
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.05
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.13
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.27
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000156814
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.36
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999848939
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.56e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:37.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35048
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 9                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    4.36
 p-value of test no 39                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.04
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.64
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.35
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.11
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.42
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.21
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.74
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.27
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  507.98
 p-value of test no 55                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.55
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.58
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.73
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.77
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.78
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.71
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4917.09
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908098
   j =  2                              :            45942
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908548
   j =  2                              :            45723
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.69
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.61
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.82
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.31
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.19
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.43
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17279.28
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.28
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.13
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.15
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.18
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.64
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.13
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.15
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.62
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.85
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.51
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.69
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.14
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.44
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.79
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.92
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.53
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.44
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.94
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.68
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.12
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.47
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.39
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.21
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.56
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.83
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.56
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.35
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.87
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.55
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.94
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.23
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.39
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.86
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4360.07
 p-value of test no 227                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3898.51
 p-value of test no 228                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.67
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.72
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.86
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999998648
 
 Normal statistic for number of bits   :  -0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.54
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999900938
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:06.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35049
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1497
 p-value of test no 4                  :  2.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334617
   j =  1                              :        599997006
   j =  2                              :             1497
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.83
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.88
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.71
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.23
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.15
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.39
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.41
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.72
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.95
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.34
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.72
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.78
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.37
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.77
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.06
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908361
   j =  2                              :            45812
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908229
   j =  2                              :            45878
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 90                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 104                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.56
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.13
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.06
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.27
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.92
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.98
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.64
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.39
 p-value of test no 133                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.73
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17278.89
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.20
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.86
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.30
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.87
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.86
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.78
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.66
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.34
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.66
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.71
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.12
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.05
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.71
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.09
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.05
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.94
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.63
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.05
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.79
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.56
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.28
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.65
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.05
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.36
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.59
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.47
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.50
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.03
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.60
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.56
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.26
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.07
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.70
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.99
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.61
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000080482
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.39
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000111883
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9968
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.20
 p-value of test no 249                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    2.38
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:06.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35050
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 5                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 11                 :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 12                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.22
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.01
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.29
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.45
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.73
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.84
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.49
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.31
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.86
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.53
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.82
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5161.50
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45557
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869557
   j =  1                              :        399908891
   j =  2                              :            45547
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907808
   j =  2                              :            46090
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 83                 :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-6
 p-value of test no 110                :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.56
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.18
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.49
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.75
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.88
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.50
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.31
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.38
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.19
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17696.75
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.82
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.66
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.76
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.27
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.47
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.68
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.36
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.02
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.68
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.70
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.63
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.07
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.58
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.16
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.96
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.47
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.88
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.93
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  129.79
 p-value of test no 170                : 1 -  3.2e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.22
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.10
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.31
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.14
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.59
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.84
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.46
 p-value of test no 177                :    0.9930
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.22
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.36
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.79
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
 p-value of test no 209                :    0.9934
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.12
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
 p-value of test no 213                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9663.91
 p-value of test no 215                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.30
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.12
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.14
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.54
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11631.00
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.46
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.37
 p-value of test no 231                :  7.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999877829
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.56
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999965405
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:37.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9990 
  78  RandomWalk1 C (L=10000, r=0)   1 -  3.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35051
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4530
 p-value of test no 14                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.01
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.62
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.33
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.77
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.43
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.76
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.15
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.85
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.76
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.93
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.45
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.36
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5170.18
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908535
   j =  2                              :            45725
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.96
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.78
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.78
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.43
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.56
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.83
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.03
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.53
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.01
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.55
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.71
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.70
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.15
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.19
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.29
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.19
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.87
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.31
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.74
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.13
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.01
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.41
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.78
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.36
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.89
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.66
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.95
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.54
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.52
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.19
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.74
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.41
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.38
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.60
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.22
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.29
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.41
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.75
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10306.04
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5111.18
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.61
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.44
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.29
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.06
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.59
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.74
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000031942
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.46
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000100027
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:40.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35052
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9928
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.98
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.65
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.12
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   86.96
 p-value of test no 53                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.59
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.74
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.67
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.51
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.50
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.47
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.26
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.52
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907711
   j =  2                              :            46140
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45566
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869566
   j =  1                              :        399908871
   j =  2                              :            45560
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.60
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.35
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.57
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.14
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.60
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.07
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.17
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 130                :  1.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    5.02
 p-value of test no 132                :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.13
 p-value of test no 133                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.10
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17174.31
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.95
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.07
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.64
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.13
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.69
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.79
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.09
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.10
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.77
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.44
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.19
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.99
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.88
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.48
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.08
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.83
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.48
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.23
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.92
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.87
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.46
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.15
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.11
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.81
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.86
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.20
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.33
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.76
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.33
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.52
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.96
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.58
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.20
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.91
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.69
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5103.40
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.79
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.73
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.17
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.95
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.42
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.53
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000056245
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.99
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000101152
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 247                : 1 -  5.2e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:53.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35053
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.68
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.44
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.90
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.45
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.25
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.84
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.87
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.52
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.63
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.15
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.99
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.62
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.78
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4861.96
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907607
   j =  2                              :            46189
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908746
   j =  2                              :            45621
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.60
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.31
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.26
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.75
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.59
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.80
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.10
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.70
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.87
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.48
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.23
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.30
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.64
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.65
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.79
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.45
 p-value of test no 153                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.75
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.19
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.07
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.12
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.80
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.00
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.30
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.32
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.18
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.67
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.87
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.89
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.14
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.19
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.52
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.80
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.90
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.97
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.71
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.55
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.11
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.84
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    2.09
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.40
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.76
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.85
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.68
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.30
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.58
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.23
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.71
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.40
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.48
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.06
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.60
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.13
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000067405
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.04
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999861131
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:36.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35054
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.76
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.68
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.95
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.50
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1324.62
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.21
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.99
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 64                 :    0.9995    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.93
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.95
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.77
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4861.60
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.19
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.42
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.81
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.82
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.85
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.56
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.08
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.47
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.97
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17516.63
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.34
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.79
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.92
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.63
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.08
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.74
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.60
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.13
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.29
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.90
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.71
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.56
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.23
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.20
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.13
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.50
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.76
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.66
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.16
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.32
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.34
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.58
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.81
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.47
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.59
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.45
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.35
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.90
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.67
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.01
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.68
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.59
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.73
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.82
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.55
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4706.17
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.81
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.05
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.50
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12084.71
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.99
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999858161
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.89
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999926921
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 238                :    0.93
 
 Sample variance                       :    2.16
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.074
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.85
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:29.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35055
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5535
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    3.75
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.81
 p-value of test no 46                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.27
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.84
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.29
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.07
 p-value of test no 52                 :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.41
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.70
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.28
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.05
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.06
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.39
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.30
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.33
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.74
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45331
 p-value of test no 70                 :    0.9948
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869331
   j =  1                              :        399909339
   j =  2                              :            45329
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45574
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908855
   j =  2                              :            45568
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.11e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.02
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.37
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.23
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.99
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.70
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.36
 p-value of test no 125                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.68
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.22
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.09
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.37
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.06
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17297.94
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.99
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.11
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.77
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.63
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.11
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.70
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.53
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.69
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.80
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.00
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.10
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.27
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.95
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.48
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.01
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.56
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.16
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.19
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.66
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.77
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.26
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.79
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.85
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.83
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.91
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.29
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.68
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.28
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.09
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.28
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.79
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.42
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10334.49
 p-value of test no 215                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.79
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.56
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.78
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.45
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.43
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.49
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.52
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000010468
 
 Normal statistic for number of bits   :   0.083
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.93
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999913373
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:04.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35056
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4176
 p-value of test no 16                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.37
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.97
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.51
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.49
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.14
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.88
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.42
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.09
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6774.96
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.46
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 62                 :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.13
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.59
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.43
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.02
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907898
   j =  2                              :            46045
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46321
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870321
   j =  1                              :        399907361
   j =  2                              :            46315
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.071
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.79
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.15
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.92
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.99
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.05
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   63.78
 p-value of test no 125                :  2.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.83
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.01
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.25
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.04
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.57
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.39
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.18
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.26
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.69
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.47
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.58
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.07
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.45
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.18
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.30
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.56
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.54
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.86
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.11
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.10
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.97
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.85
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.10
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.44
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.82
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.57
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.78
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.09
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.11
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.58
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.60
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.91
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 193                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.93
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.76
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.84
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.28
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.39
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.01
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.09
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.12
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.39
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12211.95
 p-value of test no 230                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.64
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999985835
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.20
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999935414
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:00.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35057
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 7                  :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.71
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.79
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.77
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.63
 p-value of test no 50                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.67
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.04
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.33
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.91
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.57
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.57
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.44
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.37
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.34
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.15
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.11
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908532
   j =  2                              :            45722
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908045
   j =  2                              :            45976
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.00
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.24
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.24
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.88
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.67
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.24
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.50
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.33
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.65
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.35
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.53
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.60
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.68
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.96
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.86
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.63
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.33
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.62
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.40
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.23
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.31
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.73
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.99
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.90
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.34
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.13
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.97
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.93
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.87
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.16
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.10
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.82
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.79
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.59
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.05
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.73
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.77
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.81
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.80
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.77
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.59
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.26
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.95
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.68
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.49
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.73
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.14
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.79
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12021.60
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.78
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000112870
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.88
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999940874
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 237                :  3.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.00
 p-value of test no 238                :    0.9986
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:04.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   7  CollisionOver, t = 7            4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35058
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 28                 :    0.9973
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.34
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.02
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.08
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.63
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.58
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  165.27
 p-value of test no 54                 :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.42
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.65
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.23
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.19
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.95
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.76
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.31
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45959
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869959
   j =  1                              :        399908086
   j =  2                              :            45951
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45350
 p-value of test no 71                 :    0.9933
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869350
   j =  1                              :        399909301
   j =  2                              :            45348
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 78                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 84                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.61
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.31
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.19
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.26
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.46
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9946
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.64
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.20
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.78
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.95
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17490.75
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.41
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.36
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.34
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.77
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.75
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.53
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.94
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.41
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.03
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.56
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.58
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.08
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.74
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.09
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.51
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.20
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.97
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.25
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.26
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.80
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.59
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.32
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.94
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.01
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.07
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.95
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.80
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.83
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.03
 p-value of test no 175                :  5.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.00
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.32
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.60
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.46
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.03
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.30
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 213                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.17
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.22
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.55
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.31
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4328.82
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.62
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.99
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.20
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000049831
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.59
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000009133
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :   0.068
 p-value of test no 254                : 1 -  7.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:04.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  34  Gap, r = 0                      0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35059
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.69
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.60
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.71
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.63
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.99
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.79
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.00
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.41
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.42
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.81
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.07
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.45
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908276
   j =  2                              :            45856
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908053
   j =  2                              :            45969
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.78
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.46
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.57
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.20
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.97
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.26
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.92
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.03
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.51
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.38
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.65
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.88
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.00
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.88
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.97
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.95
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.90
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.32
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.80
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.25
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.31
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.17
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.81
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.76
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.90
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  110.08
 p-value of test no 165                :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.77
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.53
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.91
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.20
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.18
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.69
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.95
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.43
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.37
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.22
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.59
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 206                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.64
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.93
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.54
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.40
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.25
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.15
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.43
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12130.92
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.06
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.48
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999979718
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.02
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999923066
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    2.08
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:56.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35060
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.51
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.25
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.96
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.53
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.91
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.51
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.05
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.52
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.84
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.53
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.26
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907814
   j =  2                              :            46087
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908255
   j =  2                              :            45862
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 88                 :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.19
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.72
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.49
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.14
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.24
 p-value of test no 124                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.10
 p-value of test no 125                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.79
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.55
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17463.69
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.30
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.45
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.39
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.13
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.96
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.20
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.63
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.83
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.26
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.23
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.23
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.05
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.86
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.11
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.58
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.15
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.73
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.84
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.74
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.38
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.17
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.16
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.11
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.38
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.77
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.26
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.64
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.04
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.09
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 205                :    0.9934
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.88
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.98
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.21
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.63
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.58
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.68
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.61
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.74
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.21
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.10
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000062830
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.90
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000136639
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.11
 p-value of test no 254                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35061
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5251
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.91
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.40
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.00
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.56
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.48
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.11
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.07
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.59
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7111.26
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.05
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.28
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.43
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.19
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.47
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908620
   j =  2                              :            45687
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907845
   j =  2                              :            46073
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 94                 :    0.9913
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 95                 :  3.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9987
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.58
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.58
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.01
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.49
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.51
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.53
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.74
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.03
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.24
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.88
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.20
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.46
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.15
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.45
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.89
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.38
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.30
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.98
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.07
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.43
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.85
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.75
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.89
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.70
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.75
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.96
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.99
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.61
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.51
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.63
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.89
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.73
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.95
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.46
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 182                :  7.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 183                :    0.98
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.87
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.25
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.36
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.72
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.18
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.01
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.40
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.71
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.21
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.85
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.26
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000123271
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.33
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999875825
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.096
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.096
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 250                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:29.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35062
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 10                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7534
 p-value of test no 15                 :  6.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.19
 p-value of test no 28                 :  7.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.71
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.69
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.42
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.69
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.93
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.70
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.65
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.75
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.89
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.23
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.62
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.49
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.13
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908649
   j =  2                              :            45668
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45431
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869431
   j =  1                              :        399909140
   j =  2                              :            45427
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
 p-value of test no 107                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.00
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.88
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.06
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.76
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.91
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.70
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.17
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.57
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.23
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.46
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.12
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.19
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.79
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.62
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.76
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.25
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.55
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.84
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.93
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.58
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.17
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.60
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.92
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.99
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.04
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.35
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.39
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.72
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.24
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.45
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.65
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.36
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.35
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.99
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.94
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.37
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.09
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.88
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.44
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.01
 p-value of test no 178                :    0.9954
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.60
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.97
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.65
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.66
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.99
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.14
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.77
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.85
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.17
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.38
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.57
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999937985
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.17
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000081952
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 248                :    0.01
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:24.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35063
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.25
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.84
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.91
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.04
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.33
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.81
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.02
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.98
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.75
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.42
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.00
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.14
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.65
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908158
   j =  2                              :            45918
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907993
   j =  2                              :            45996
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.67
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.19
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.62
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.38
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.96
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.10
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.83
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.60
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.17
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.79
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.82
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.89
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.75
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.84
 p-value of test no 149                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.15
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.17
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.96
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.85
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.96
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.73
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.05
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.84
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.47
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.54
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.87
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.04
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.78
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.76
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.68
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.14
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.42
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.54
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.44
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.26
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.08
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.04
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.40
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.38
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.45
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.01
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.36
 p-value of test no 196                :    0.9948
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.85
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 204                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 205                :  6.6e-4    *****
 
 Anderson-Darling statistic = A2       :    9.10
 p-value of test no 206                :  3.9e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  295.61
 p-value of test no 207                :  1.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.60
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 213                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10278.32
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.16
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.63
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.30
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.68
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.81
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.48
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.41
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999939806
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.32
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000036205
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:57.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        1.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35064
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    5.98
 p-value of test no 39                 :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.11
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.97
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.22
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.96
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.41
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.20
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.08
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.14
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.76
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.75
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.80
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45525
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869525
   j =  1                              :        399908954
   j =  2                              :            45517
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908231
   j =  2                              :            45877
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-6
 p-value of test no 113                :    0.9987
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.11
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.04
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.77
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.25
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.59
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.91
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.38
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17700.82
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.20
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.15
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.91
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.03
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.59
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.63
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.26
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.90
 p-value of test no 157                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.26
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.83
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.61
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.64
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.01
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.60
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.00
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.05
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.62
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.12
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.79
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.52
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.29
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.50
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.65
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.91
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.85
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.20
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.45
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    2.35
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 195                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.01
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.36
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.17
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.79
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.06
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.91
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.21
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.75
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.49
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.96
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.95
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.87
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999952289
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.57
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999941180
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:21.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35065
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.76
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.56
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.86
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.26
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.38
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.43
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1354.95
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7175.19
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.94
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.94
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.51
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.65
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4896.51
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908437
   j =  2                              :            45780
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907631
   j =  2                              :            46180
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.24
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.02
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.95
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.79
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.92
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.01
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.57
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.72
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.49
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.27
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.31
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.46
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.29
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.45
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.10
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.94
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.09
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.93
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.27
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.28
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.58
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.89
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.59
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.76
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.45
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.41
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.13
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.18
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.78
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.82
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.90
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.74
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.31
 p-value of test no 175                :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.66
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.60
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.70
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.42
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10291.66
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.93
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.43
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.88
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3954.34
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.55
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.13
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.47
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000024088
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.25
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000182746
 
 Normal statistic for number of bits   :    1.44
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 250                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 253                :  5.6e-3
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35066
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5502
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4152
 p-value of test no 16                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9964
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    4.02
 p-value of test no 39                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.45
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.08
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.90
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.04
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.41
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.75
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.23
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6960.11
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.15
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.61
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.60
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.16
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.88
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45440
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869440
   j =  1                              :        399909123
   j =  2                              :            45434
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 73                 :    0.9955
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 74                 :  4.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9977
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 84                 :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 99                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.53
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.30
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.84
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.00
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.68
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.40
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.30
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.04
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.01
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.57
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.68
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.01
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.94
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.95
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.83
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.65
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.75
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.86
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.70
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.80
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.49
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.66
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.59
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.46
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.80
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.40
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.96
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.70
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.32
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.84
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.50
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.54
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.56
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.54
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.65
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.20
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.00
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.41
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.45
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.83
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.72
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.37
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.33
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.30
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.46
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.18
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.08
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.33
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.34
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999981158
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.51
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999995078
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:28.82
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35067
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    4.30
 p-value of test no 27                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     179
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.08
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.81
 p-value of test no 49                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.03
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.93
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.55
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.61
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1347.26
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7210.11
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.06
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.51
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.95
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.54
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45447
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869447
   j =  1                              :        399909110
   j =  2                              :            45439
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907657
   j =  2                              :            46167
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 73                 :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.70
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.81
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.70
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.01
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.91
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.08
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.29
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.36
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.37
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.85
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.19
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.55
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.23
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.70
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.39
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.42
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.99
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.57
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.20
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.85
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.90
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.85
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.37
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.59
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.60
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.39
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.68
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.53
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.43
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.10
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.33
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.77
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.53
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.92
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.35
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.27
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.46
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.34
 p-value of test no 174                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.24
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.48
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.44
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.55
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.83
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.02
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.05
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.79
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.75
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.86
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.25
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.45
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.86
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.79
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000101974
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.03
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000019231
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.048
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.02
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.067
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35068
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.38
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.89
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.29
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.99
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.63
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.74
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.54
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.14
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.05
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.98
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.04
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908067
   j =  2                              :            45965
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-3
 p-value of test no 72                 :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 77                 :    0.9924
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.66
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.53
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.65
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.34
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.06
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.85
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.22
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.41
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.33
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.02
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17146.42
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.02
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.65
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.28
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.61
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.42
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.26
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.34
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.55
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.38
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.27
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.57
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.00
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.34
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.27
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.67
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.95
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.88
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.22
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.37
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.61
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.62
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.26
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.20
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.51
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.32
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.29
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.36
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.38
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.84
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.40
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.43
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.97
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10102.51
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.65
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.81
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.23
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4308.39
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.22
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.43
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.49
 p-value of test no 231                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999802541
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.77
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000009337
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:55.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35069
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 10                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.69
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.54
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.35
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.05
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.03
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.94
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.59
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.98
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.55
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.44
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.49
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.99
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908675
   j =  2                              :            45658
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908102
   j =  2                              :            45943
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.84
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.03
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.46
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.43
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.32
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.63
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.04
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.93
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17401.34
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.40
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.29
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.44
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.19
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.84
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.96
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.91
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.24
 p-value of test no 153                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.31
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.60
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.38
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.64
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.64
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.86
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.29
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.66
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.93
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.30
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.81
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.68
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.14
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.47
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.92
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.97
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.13
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.30
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.32
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.83
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.78
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.31
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.87
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.52
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.70
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.85
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
 p-value of test no 204                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.07
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.80
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.12
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.06
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 223                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5113.43
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.64
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.53
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.85
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11601.85
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.60
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999932945
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.23
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999839690
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    2.55
 p-value of test no 254                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35070
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9955
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.44
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.55
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.02
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.98
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.13
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.96
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.02
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.96
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.48
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.92
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.48
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.52
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908330
   j =  2                              :            45826
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
 p-value of test no 72                 :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 94                 :    0.9928
 
 Anderson-Darling statistic = A2       :    4.44
 p-value of test no 95                 :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9990
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.59
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.76
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.80
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.14
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.21
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.69
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.69
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.28
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.50
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.72
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.32
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17787.11
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.08
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.02
 p-value of test no 147                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.13
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.71
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.07
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.13
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.38
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.76
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.86
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.84
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.34
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.07
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.07
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.08
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.66
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.64
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.55
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4803.78
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.11
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.07
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.31
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.74
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.57
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.39
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.88
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.43
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.27
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.63
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.19
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.22
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.037
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.53
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.60
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.97
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4302.84
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.67
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.69
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.21
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000049201
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.91
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000048175
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35071
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 4                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 10                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 12                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.26
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.28
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.15
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.32
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.42
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1556.02
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.92
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.70
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.89
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.72
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.12
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907779
   j =  2                              :            46103
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907960
   j =  2                              :            46017
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.18
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.07
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.97
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.49
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.49
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 138                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 140                :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.82
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.20
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.45
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.22
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.32
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.46
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.25
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.17
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.65
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.48
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.63
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.93
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.73
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.89
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.20
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.39
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.43
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.15
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.58
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.75
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.16
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.55
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.12
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.50
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.56
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.84
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.56
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.02
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.57
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.22
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.37
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.02
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.60
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.12
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.86
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.08
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.21
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000036502
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.31
 p-value of test no 233                :  9.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999989810
 
 Normal statistic for number of bits   :  -0.081
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 251                :    0.9921
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.69
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35072
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.79
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    3.10
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.93
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.24
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.90
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.92
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.46
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.23
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.07
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7208.62
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.18
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.31
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.34
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.67
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.91
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908296
   j =  2                              :            45849
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908071
   j =  2                              :            45960
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.76
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.53
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.61
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.56
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.85
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.18
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.67
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.86
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17033.47
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.44
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.17
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.30
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.01
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.40
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.28
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.81
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.54
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.35
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.16
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.14
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.41
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.83
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.94
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.02
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.60
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.36
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.79
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.66
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.44
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.63
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.69
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.98
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.41
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.46
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.69
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.50
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.17
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.62
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.08
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.10
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.69
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.52
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.45
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.64
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.50
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11594.57
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.22
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999972203
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.02
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000119146
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:54.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35073
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    3.80
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     969
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.90
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.66
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.85
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.86
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.66
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.14
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.23
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.62
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.99
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.08
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4886.63
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45744
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869744
   j =  1                              :        399908517
   j =  2                              :            45734
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45359
 p-value of test no 71                 :    0.9925
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869359
   j =  1                              :        399909284
   j =  2                              :            45355
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 98                 :  2.5e-4    *****
 
 Anderson-Darling statistic = A2       :    3.90
 p-value of test no 99                 :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.78
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.40
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.18
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.25
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.57
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.24
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.84
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.67
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.37
 p-value of test no 141                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.66
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.21
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.67
 p-value of test no 149                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.03
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.43
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.61
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.30
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.67
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.45
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.13
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.21
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.88
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.35
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.55
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.17
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.78
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.76
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.94
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.24
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.38
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.82
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.58
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.04
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.69
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.56
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.10
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.98
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.63
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.58
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.23
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.70
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10230.38
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.81
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 220                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.46
 p-value of test no 221                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5138.68
 p-value of test no 222                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.25
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.90
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.10
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.00
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.12
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.65
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999985925
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.15
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999962942
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35074
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5517
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    4.01
 p-value of test no 36                 :  8.7e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     251
 p-value of test no 37                 :    0.9980
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.65
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.52
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.75
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.93
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.08
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7126.35
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.78
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.43
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.15
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.27
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.61
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908146
   j =  2                              :            45918
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908460
   j =  2                              :            45764
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.28
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.32
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.30
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.26
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.68
 p-value of test no 124                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.49
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.71
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.39
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.13
 p-value of test no 137                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.17
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.64
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.52
 p-value of test no 147                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.29
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.93
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.93
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.98
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.10
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.77
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.19
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.06
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.12
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.74
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.74
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.11
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.49
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.40
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.17
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.43
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.48
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.65
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.66
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.48
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.99
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.97
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.52
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.31
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.04
 p-value of test no 174                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.62
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.05
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.34
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.11
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.49
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.22
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.56
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.71
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.80
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.78
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.43
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.11
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.17
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000093625
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.22
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999900329
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 251                :    0.9953
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35075
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5236
 p-value of test no 13                 :    0.9941
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.65
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.16
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.15
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.87
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.46
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.54
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.67
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.51
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.71
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.34
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.62
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.90
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46326
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870326
   j =  1                              :        399907353
   j =  2                              :            46316
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45788
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869788
   j =  1                              :        399908429
   j =  2                              :            45778
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.92
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.12
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.40
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.42
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.48
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.33
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.14
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.02
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17633.35
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.78
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.83
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.04
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.26
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.84
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.09
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.64
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.01
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.52
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.78
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.29
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.43
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.51
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.43
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.21
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.58
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.76
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.55
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.61
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.44
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.84
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.51
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.04
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.40
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.63
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.21
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.99
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.43
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.40
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.59
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.72
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.79
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.75
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10265.75
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.29
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.02
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.33
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.99
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.71
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.08
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000009634
 
 Normal statistic for number of bits   :   0.076
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.14
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999973526
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35076
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 5                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4164
 p-value of test no 14                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.02
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.76
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.13
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.62
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.05
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.33
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.31
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6829.32
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.24
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.25
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.22
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.37
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.34
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46118
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870118
   j =  1                              :        399907767
   j =  2                              :            46112
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9903
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.44
 p-value of test no 119                :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.18
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.96
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.25
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.12
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.77
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.88
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.14
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17164.33
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.70
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.31
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.05
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.82
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.71
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.38
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.20
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.93
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.96
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.17
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.29
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.56
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.97
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.98
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.80
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.48
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.46
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.79
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.90
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.80
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.44
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.39
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.08
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.91
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.37
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.01
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.84
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.29
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.68
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.97
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.65
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.02
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.75
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.88
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.22
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.45
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4328.20
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.16
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12266.14
 p-value of test no 230                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.38
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000038941
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.17
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999991097
 
 Normal statistic for number of bits   :  -0.070
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    2.18
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35077
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 12                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4181
 p-value of test no 16                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7582
 p-value of test no 20                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.25
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.82
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.49
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.19
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.63
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.54
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.61
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.18
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.00
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.97
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.20
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.39
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.49
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.96
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908453
   j =  2                              :            45766
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46181
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870181
   j =  1                              :        399907641
   j =  2                              :            46175
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.36
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.88
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.86
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.83
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.91
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.28
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.27
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.70
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.91
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.25
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.91
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.68
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.04
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.64
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.54
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.52
 p-value of test no 154                :    0.9920
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.07
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.39
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.95
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.17
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.60
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.45
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.30
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.29
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.47
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.60
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.45
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.39
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.27
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.19
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.43
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.09
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.41
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.09
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.73
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.15
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.38
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.26
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.12
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.31
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.63
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.17
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.50
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.23
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11638.91
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.52
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.50
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999899147
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999980657
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:44.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35078
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4186
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.98
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.92
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.48
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.17
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.12
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1521.05
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6859.44
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.93
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.88
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.49
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.29
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908453
   j =  2                              :            45772
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45542
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869542
   j =  1                              :        399908917
   j =  2                              :            45540
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 101                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.04e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.86
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.64
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.84
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.73
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.91
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.50
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.27
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.02
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.80
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.07
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.21
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.15
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.21
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.98
 p-value of test no 150                :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.44
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.50
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.09
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.24
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.40
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.70
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.50
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.60
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.52
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.13
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.32
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.04
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.43
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.27
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.33
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.45
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.48
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.52
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.81
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.24
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.33
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.00
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.32
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.47
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5096.96
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.58
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.31
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.94
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.68
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11911.25
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.16
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000025108
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.20
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999948446
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35079
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.99
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.14
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.87
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.12
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.46
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.51
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.58
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.67
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.82
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.46
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.83
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.79
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.46
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5123.07
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45552
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869552
   j =  1                              :        399908898
   j =  2                              :            45548
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907901
   j =  2                              :            46042
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.13
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.67
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.56
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.16
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.35
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.64
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.10
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 139                :    0.9924
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.04
 p-value of test no 141                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.14
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.18
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.79
 p-value of test no 149                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.97
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.91
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.23
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.79
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.20
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.42
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.48
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.50
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.86
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.36
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.46
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.25
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.26
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.41
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.85
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.67
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.38
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.95
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.61
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.66
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.25
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5199.83
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.12
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.95
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.93
 p-value of test no 183                :    0.03
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.82
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.40
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.47
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10150.80
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.63
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.16
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.40
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.76
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.34
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11930.92
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.97
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999940154
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999827483
 
 Normal statistic for number of bits   :   -1.36
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.70
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35080
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 8                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7108
 p-value of test no 15                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.63
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.16
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.95
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.18
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.69
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.31
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.96
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.48
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.08
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-3
 p-value of test no 59                 :    0.9981
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.79
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.52
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.71
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.66
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908629
   j =  2                              :            45684
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.52
 p-value of test no 117                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.82
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.39
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.38
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.06
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.15
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.52
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.16
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.33
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.27
 p-value of test no 136                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.08
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.85
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.71
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.42
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.68
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.38
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.35
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.00
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.54
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.10
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.42
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.60
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.02
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.46
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.25
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.22
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.06
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.57
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.50
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.78
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.27
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.55
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.89
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.51
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.87
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.59
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.17
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  272.78
 p-value of test no 174                : 1 -  1.2e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.81
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.13
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.85
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.87
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.68
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 206                :    0.9957
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.47
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.78
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.43
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.62
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.67
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.18
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.91
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.09
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.02
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.83
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000082765
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.22
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999865136
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:34.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)  1 -  1.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35081
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 7                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.56
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.73
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.20
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.65
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.80
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.84
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.14
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.31
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.98
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.43
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.09
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.49
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.33
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908453
   j =  2                              :            45769
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908053
   j =  2                              :            45966
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.14
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.55
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.79
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.89
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.59
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.75
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.99
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.78
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.47
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.02
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17280.62
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.01
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.30
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.96
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.59
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.30
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.62
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.80
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.77
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.93
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.09
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.79
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.97
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.59
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.57
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.16
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.21
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.27
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.71
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.10
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.76
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.85
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.37
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.97
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.23
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.59
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.29
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.93
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.04
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9713.01
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.66
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.80
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.52
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.16
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.70
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11727.52
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.69
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999957353
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.75
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999922763
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.063
 p-value of test no 253                :    0.47
 
 Sample variance                       :    2.22
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:32.27
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35082
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 4                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5352
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7578
 p-value of test no 15                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.21
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.89
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.56
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.16
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.76
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.05
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.32
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.87
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7103.32
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.86
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.80
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.11
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.54
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.48
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907726
   j =  2                              :            46134
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908497
   j =  2                              :            45747
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.93
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.00
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.56
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.30
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.12
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.57
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.81
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.04
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.76
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.24
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.37
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.81
 p-value of test no 148                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.61
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.45
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.42
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.12
 p-value of test no 155                :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.00
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.37
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.32
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.65
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.19
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.09
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.48
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.90
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.36
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.31
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.72
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.29
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.38
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.07
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.61
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.91
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.09
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.14
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.73
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.06
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.43
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.45
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.67
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.00
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.77
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.97
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.36
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.50
 p-value of test no 218                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.92
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.12
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.14
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.62
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.69
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.93
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.60
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000124852
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.08
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000141886
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:48.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35083
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4176
 p-value of test no 16                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.40
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.59
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.80
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.72
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.80
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.07
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.22
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.34
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.08
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.04
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.62
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.94
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.35
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.18
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908317
   j =  2                              :            45834
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45373
 p-value of test no 71                 :    0.9910
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869373
   j =  1                              :        399909256
   j =  2                              :            45369
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.30
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.96
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.35
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.63
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.01
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.74
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.63
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.92
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.96
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.04
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.11
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.82
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.25
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.28
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.30
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.91
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.83
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.97
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.62
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.21
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.06
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.91
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.16
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.86
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.35
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.94
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.18
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.90
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.42
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.03
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.82
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.44
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.44
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.93
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4800.82
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.80
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.76
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.90
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.33
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.84
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.09
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.42
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.81
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.68
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5112.58
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.47
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.78
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3884.59
 p-value of test no 228                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.88
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.43
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.78
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999993779
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.84
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999935903
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
 p-value of test no 236                : 1 -  2.2e-5    *****
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 238                :    0.99
 
 Sample variance                       :    2.06
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 240                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 243                :  6.5e-3
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 246                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 247                :  6.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.40
 p-value of test no 248                :  8.3e-3
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:07.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35084
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 12                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5519
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9947
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.74
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.99
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.95
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.70
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.25
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.71
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.44
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.84
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1332.42
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6801.43
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.71
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.36
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.56
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.59
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.76
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908425
   j =  2                              :            45783
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908333
   j =  2                              :            45832
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 105                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.45
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.09
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.50
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.19
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.70
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.70
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.83
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.19
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17142.73
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.92
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.98
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.02
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.16
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.83
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.31
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.80
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.11
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.92
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.08
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.31
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.69
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.72
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.58
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.49
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.14
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.86
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.19
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.89
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.15
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.42
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.57
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.75
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.12
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.44
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 185                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.40
 p-value of test no 198                :    0.9942
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.05
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.02
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.48
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.18
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.37
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.97
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.91
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.44
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.19
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12047.32
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.14
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999836006
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.22
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999936074
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.089
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35085
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.74
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.66
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.74
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.86
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  190.50
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.35
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1535.53
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.31
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 59                 :    0.9965
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.58
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.61
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.62
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.71
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907955
   j =  2                              :            46018
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908213
   j =  2                              :            45883
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 103                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.61
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.22
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.94
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.77
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.03
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.29
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.24
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.14
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.06
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.45
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.23
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.01
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.32
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.66
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.57
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.18
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.16
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.93
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.74
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.59
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.60
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.84
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.88
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.13
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.93
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.72
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.35
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.27
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.37
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.76
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.55
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.08
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.86
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.88
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.81
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9915
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.53
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.48
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.34
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.96
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.25
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.25
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.13
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.11
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.21
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11482.52
 p-value of test no 229                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.61
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.84
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000064333
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000032563
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.14e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35086
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.53
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.46
 p-value of test no 48                 :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.50
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.82
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.44
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.58
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.88
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6873.96
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.09
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.83
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.09
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.38
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907919
   j =  2                              :            46036
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.9e-3
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.74e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.95
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.20
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.00
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.15
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.34
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.19
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.35
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.89
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.76
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.25
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.30
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.23
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.86
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.11
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.19
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.47
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.83
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.59
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.81
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.77
 p-value of test no 159                :  6.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.70
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.00
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.32
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.77
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.51
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.19
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.22
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.52
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.72
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.62
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.52
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.30
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.38
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.56
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.10
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 7.45e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.30
 p-value of test no 178                :  9.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.10
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.70
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.92
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.68
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.69
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.43
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.97
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.40
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.64
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12052.20
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.19
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000120628
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.48
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999911705
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35087
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 10                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    3.46
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.46
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.30
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.81
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.40
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.04
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.42
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.63
 p-value of test no 53                 :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.23
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.38
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.94
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.14
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.17
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.71
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.64
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.25
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.74
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46270
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870270
   j =  1                              :        399907463
   j =  2                              :            46264
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45839
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869839
   j =  1                              :        399908327
   j =  2                              :            45829
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.74e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.23
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.66
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.63
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.09
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.27
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.59
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.30
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.92
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.49
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.77
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.74
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.68
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.24
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.21
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.35
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.68
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.29
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.21
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.58
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.92
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.78
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.12
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.83
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.09
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.12
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.16
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.46
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.79
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.84
 p-value of test no 167                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.92
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.98
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.21
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.19
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.81
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.00
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.22
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.36
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.25
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.049
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.67
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.55
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.00
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.43
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.59
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4694.08
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.97
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.19
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.13
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.33
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.72
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999960569
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.77
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999947315
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.83
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.10
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:22.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35088
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.89
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.83
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.52
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.60
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.84
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.67
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.88
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.99
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.37
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.46
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.99
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.72
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.60
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.75
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.29
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907739
   j =  2                              :            46129
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.01
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.31
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.79
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.02
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.81
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.67
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.47
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 139                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.73
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17387.02
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.99
 p-value of test no 146                :  9.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.81
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.98
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.06
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.34
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.85
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.62
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.50
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.14
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.43
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.70
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.34
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.13
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.65
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.87
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.87
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.79
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.52
 p-value of test no 167                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.31
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.39
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.12
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.31
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.08
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.70
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.13
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.81
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.17
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.23
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.21
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.10
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.29
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.88
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.65
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.81
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.56
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.82
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.30
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.52
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999914453
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999959351
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35089
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5359
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.88
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.66
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.54
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.40
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.02
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.23
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.83
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.36
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.60
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.01
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 62                 :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.24
 p-value of test no 65                 :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.86
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.11
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.88
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908168
   j =  2                              :            45907
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908246
   j =  2                              :            45871
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
 p-value of test no 100                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.94
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.13
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.09
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.88
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.58
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.39
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.23
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.51
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.81
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.83
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.64
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.81
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.33
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.75
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.83
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.44
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.61
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.04
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.41
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.43
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.63
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.19
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.79
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.29
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.16
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.83
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.17
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5142.27
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.00
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.57
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.74
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.68
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.72
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.26
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.31
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.42
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.79
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.93
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.74
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.90
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.13
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.18
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.11
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.34
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.96
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.28
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.01
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.82
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11513.47
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.77
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999678899
 
 Normal statistic for number of bits   :   -2.54
 p-value of test no 232                :    0.9944
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.97
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000143116
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:21.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35090
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 15                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 27                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    3.31
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.82
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.45
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.31
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.49
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.68
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.52
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6904.12
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.66
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.85
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.84
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.56
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.49
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908535
   j =  2                              :            45731
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46143
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870143
   j =  1                              :        399907718
   j =  2                              :            46135
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.54
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.83
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.35
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.30
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.67
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.29
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.20
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.94
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.07
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.93
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.04
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.65
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.67
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.46
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.46
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.19
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.76
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.73
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.75
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.17
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.94
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.35
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.54
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.08
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.33
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.48
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.42
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.25
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.89
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.61
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.69
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.30
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.68
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.54
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.81
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.19
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.63
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.07
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.90
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.12
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.99
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.05
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.59
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.03
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.61
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.51
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.29
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.34
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.26
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.44
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.63
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.19
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000122671
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.52
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999985286
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35091
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 8                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    3.61
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.44
 p-value of test no 41                 :  7.0e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    3.01
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.59
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.95
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.04
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.24
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.57
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.17
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.96
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.90
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.13
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  7.1e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.17
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.19
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.53
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.60
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.56
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45544
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908914
   j =  2                              :            45540
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.55
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.31
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.32
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.57
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.37
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.22
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.21
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.15
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.02
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.13
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.60
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.37
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.01
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.24
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.64
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.19
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.40
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.14
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.47
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.24
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.47
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.44
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.04
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.13
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.71
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.51
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.23
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.72
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.22
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.44
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.75
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.65
 p-value of test no 172                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.97
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.81
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.14
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.38
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.94
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.85
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.08
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.48
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.53
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 213                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9747.32
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.18
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.18
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.07
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.84
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.68
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11496.72
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.38
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999996452
 
 Normal statistic for number of bits   :  -0.028
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.53
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000003331
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.26
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
 p-value of test no 246                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            0.9990 
  25  ClosePairs mNP, t = 16          7.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35092
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    3.98
 p-value of test no 38                 :  8.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.26
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.74
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.08
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.70
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.17
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.60
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.58
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.45
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.51
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.95
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.03
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.94
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.29
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.95
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.51
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45729
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869729
   j =  1                              :        399908546
   j =  2                              :            45721
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908732
   j =  2                              :            45628
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.77
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.60
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.95
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.34
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.60
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.45
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.74
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.23
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.72
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.17
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.14
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.86
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.69
 p-value of test no 149                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.62
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.60
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.56
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.89
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.20
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.10
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.33
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.88
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.37
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.64
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.72
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.34
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.24
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.65
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.96
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.22
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.22
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.70
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.92
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.13
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.91
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.59
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.47
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.01
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.69
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.79
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.64
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.18
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.15
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.56
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.94
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.19
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4703.00
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.46
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.60
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.09
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11489.38
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.76
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000090769
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.92
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999978581
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35093
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997366
   j =  2                              :             1314
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.84
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.62
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.33
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.79
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.52
 p-value of test no 53                 :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.13
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.80
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.93
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.54
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.24
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.26
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.74
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.97
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.13
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908354
   j =  2                              :            45820
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908674
   j =  2                              :            45660
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
 p-value of test no 107                :    0.9901
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.47
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.00
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.94
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.59
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.09
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.13
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.96
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 128                :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.59
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.51
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.18
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.92
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17204.24
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.69
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.74
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.19
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.53
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.72
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.29
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.28
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.11
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.12
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.85
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.98
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.37
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.68
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.71
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.14
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.31
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.17
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.98
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.92
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.65
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.06
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.66
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.16
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.63
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.03
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.87
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.50
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.70
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.10
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 195                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.28
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.97
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.77
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 213                :    0.9944
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9667.18
 p-value of test no 215                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.03
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.22
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.53
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.78
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.19
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.11
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.41
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999961790
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999851726
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 250                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  85  Fourier3, r = 27                0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35094
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 11                 :    0.9977
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     531
 p-value of test no 31                 :    0.9978
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.10
 p-value of test no 35                 :  8.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.21
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.43
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.38
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.47
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.27
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.51
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.13
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.98
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.31
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.10
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.12
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.81
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4810.27
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908629
   j =  2                              :            45684
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46271
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870271
   j =  1                              :        399907460
   j =  2                              :            46267
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.09e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.57
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.14
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.89
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.76
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.99
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.99
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.66
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.92
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.37
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17110.86
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.81
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.46
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.74
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.48
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.90
 p-value of test no 151                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.79
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.24
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.74
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.97
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.76
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.82
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.85
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.36
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.94
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.19
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.70
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.30
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.12
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.20
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.32
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.37
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.70
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.24
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.31
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.55
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.46
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.31
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.02
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.22
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.75
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.31
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.71
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
 p-value of test no 212                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10280.89
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.46
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.74
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.97
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.76
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11547.43
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.54
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.62
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999927302
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.09
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000013378
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.040
 p-value of test no 238                :    0.48
 
 Sample variance                       :    2.36
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35095
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 7                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.64
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.32
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.60
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.34
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.01
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.80
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.44
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.54
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.75
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.18
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.43
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.11
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5223.05
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908153
   j =  2                              :            45922
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908638
   j =  2                              :            45678
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.98
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.59
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.37
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.56
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.62
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.90
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.82
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.68
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.68
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.15
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.47
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   49.35
 p-value of test no 149                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.44
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.04
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.54
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.57
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.37
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.66
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.71
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.81
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.91
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.75
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.86
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.21
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.57
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.53
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.30
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.51
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.33
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.71
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.04
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.80
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.79
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.50
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.33
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.70
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 182                :    0.9974
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.23
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.40
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.73
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.94
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.53
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.16
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.83
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.36
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.78
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.13
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.49
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.11
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000080248
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.82
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999823301
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.80e-4
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35096
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 8                  :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.26
 p-value of test no 47                 :  7.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.12
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.94
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.37
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.70
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.85
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1524.52
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.91
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.69
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.77
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.22
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.52
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4915.26
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908104
   j =  2                              :            45939
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907613
   j =  2                              :            46183
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.96
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  109.83
 p-value of test no 120                :  7.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.11
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.03
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.54
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.57
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 131                :    0.9918
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.83
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.92
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 143                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17741.36
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.55
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.42
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.20
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.02
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.24
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.81
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.81
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.77
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.69
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.01
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.13
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.72
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.55
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.71
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.85
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.10
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.82
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.96
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.21
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.87
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.18
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.18
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.61
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.20
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5155.85
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.85
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.25
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.27
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 182                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.61
 p-value of test no 183                :  4.5e-3
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    2.08
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.83
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.42
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10266.13
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.16
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.49
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.81
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.08
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.42
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.70
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.25
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.75
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999968837
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.63
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000053173
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:08.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  60  WeightDistrib, r = 20           7.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35097
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 4                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.15
 p-value of test no 35                 :  2.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.17
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.78
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.76
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.05
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.46
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6755.95
 p-value of test no 57                 :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.09
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.45
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.30
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.81
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.72
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908602
   j =  2                              :            45696
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908582
   j =  2                              :            45703
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.25
 p-value of test no 119                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.91
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.80
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.25
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.18
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.78
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.29
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.15
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.94
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.24
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.89
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17216.37
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.87
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.43
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.42
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.92
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.99
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.03
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.39
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.62
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.87
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.31
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.36
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.87
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.91
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.81
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.71
 p-value of test no 166                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.61
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.73
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.03
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.67
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.94
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.19
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.70
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.03
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.05
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.23
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.10
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.11
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.15
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.028
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.68
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.13
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.79
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.31
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.41
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.00
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.94
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000106426
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.98
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999667091
 
 Normal statistic for number of bits   :   -2.63
 p-value of test no 234                :    0.9958
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 240                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 243                :    0.98
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:31.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35098
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 11                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    3.65
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.08
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.41
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.46
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.95
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.42
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.81
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.18
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.56
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.04
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.93
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.24
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.08
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.04
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45694
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908614
   j =  2                              :            45690
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908415
   j =  2                              :            45788
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
 p-value of test no 100                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.49
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.05
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.71
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.33
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.94
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.33
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.47
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.90
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.23
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17705.52
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.11
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.99
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.78
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.53
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.65
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.95
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.47
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.48
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.95
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.14
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.50
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.43
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.06
 p-value of test no 161                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.74
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.88
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.74
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.08
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.13
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.83
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5067.75
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.48
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.92
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.65
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.37
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.68
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.12
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.44
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.63
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    2.30
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.64
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.06
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.27
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.08
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.19
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.68
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.20
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.87
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.63
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.61
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.91
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.10
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999861101
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.85
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999963716
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 238                :    0.97
 
 Sample variance                       :    2.00
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:29.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35099
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 16                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.11
 p-value of test no 34                 : 1 -  7.2e-5    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.37
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.56
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.72
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.49
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.70
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.41
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.41
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.62
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.36
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.11
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.09
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.96
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46361
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870361
   j =  1                              :        399907285
   j =  2                              :            46347
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907658
   j =  2                              :            46168
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.31
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.55
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.40
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.87
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.81
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.70
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.87
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.18
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.20
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.29
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.70
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.52
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.55
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.45
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.51
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.89
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.04
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.10
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.30
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.11
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.94
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.99
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.92
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.71
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.45
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.44
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.62
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.81
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.01
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.00
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.82
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.79
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.99
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.45
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.78
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.85
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.92
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.97
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.01
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.08
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.25
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.65
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.27
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4191.22
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.62
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.78
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.27
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000033643
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.24
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999799643
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9905
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:27.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9           1 -  7.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35100
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.57
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.38
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.29
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.59
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.70
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.41
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.79
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.26
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.43
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7283.21
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.13
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.81
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.60
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.96
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.30
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908159
   j =  2                              :            45913
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908383
   j =  2                              :            45804
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
 p-value of test no 86                 :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-4
 p-value of test no 112                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.21
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.13
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.94
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.17
 p-value of test no 122                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.10
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.61
 p-value of test no 124                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.73
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.69
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
 p-value of test no 131                :    0.9953
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.65
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.13
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.93
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17259.32
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.89
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.14
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.04
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.56
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.59
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.95
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.66
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.13
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.44
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.70
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.49
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.26
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.60
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.24
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.23
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.77
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.48
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.60
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.82
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.86
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.77
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.09
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.10
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.12
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.18
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.25
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.72
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.06
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.14
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.15
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.77
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.94
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.35
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.98
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3951.59
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.14
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.49
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11594.83
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.68
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000089299
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.87
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000079333
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :  9.1e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:41.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35101
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 23                 :    0.9977
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.13
 p-value of test no 26                 :    0.9995    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.34
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.11
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.17
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.03
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.79
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.62
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.66
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.82
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.26
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.44
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.76
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.14
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.72
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.99
 p-value of test no 67                 :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4981.68
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907725
   j =  2                              :            46133
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907786
   j =  2                              :            46098
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.94
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.65
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.27
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.66
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.18
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.03
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.30
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.74
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.74
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.70
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17756.51
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.37
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.04
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.57
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.68
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.81
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.11
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.40
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.37
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.43
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.52
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  579.83
 p-value of test no 158                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.43
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.82
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.96
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.53
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.23
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.61
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.63
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.18
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.76
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.56
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.14
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.98
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.69
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.57
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.64
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.60
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  154.25
 p-value of test no 175                :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.05
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.46
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.16
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.34
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.39
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.56
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.74
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.34
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.39
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.41
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.31
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.99
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.33
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.19
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11519.64
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.09
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000126742
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999937541
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:32.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2, t = 3          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35102
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.89
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.98
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.51
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.52
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.02
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.50
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.95
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.10
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.13
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.99
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.03
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.92
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45516
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908969
   j =  2                              :            45514
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908928
   j =  2                              :            45530
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.43
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.84
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.36
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.24
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.52
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.71
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.16
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.92
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17696.46
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.74
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.80
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.90
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.20
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.74
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.30
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.02
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.80
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.51
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.26
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.92
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.61
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.72
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.30
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.48
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.74
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.70
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.62
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.62
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.58
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.42
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.98
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.92
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.04
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.23
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.73
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.98
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.76
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.68
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.62
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.66
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.61
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9736.64
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.06
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-3
 p-value of test no 223                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5142.07
 p-value of test no 226                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.01
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.40
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.11
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12090.04
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.47
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999922145
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.46
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000071104
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9901
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:29.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35103
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.96
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.58
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.12
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.29
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.08
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.66
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.35
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6835.23
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.70
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.68
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.88
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.16
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.16
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908489
   j =  2                              :            45754
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908616
   j =  2                              :            45692
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 97                 :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.46
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.36
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.33
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.34
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.93
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 132                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.12
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.98
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.85
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.94
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.50
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.96
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.88
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.98
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.33
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.59
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.76
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.17
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.21
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.76
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.07
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.82
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.08
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.23
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.10
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.90
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.51
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.25
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.75
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.86
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.02
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.87
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.73
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.80
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.85
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.27
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.54
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.31
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.22
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12082.78
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.08
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.37
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999989348
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.62
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999970661
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:51.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35104
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    3.79
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.63
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.14
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.12
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.67
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.56
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.47
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.21
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.42
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.83
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6834.88
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.65
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.49
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.92
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.20
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.94
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908097
   j =  2                              :            45947
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45523
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908958
   j =  2                              :            45515
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.48
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.59
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.69
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.07
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.40
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.29
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.10
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.35
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.91
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.66
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.02
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.89
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.37
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.50
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   57.08
 p-value of test no 153                :  2.6e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   48.56
 p-value of test no 154                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.02
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.80
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.95
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.75
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.49
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.31
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.89
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.51
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.67
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.09
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.51
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.10
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.42
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.17
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.92
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.90
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.85
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.73
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.92
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.73
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.49
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.65
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.53
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.02
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.92
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.55
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.45
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.02
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.24
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.57
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.46
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.21
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999997910
 
 Normal statistic for number of bits   :  -0.017
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.34
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999899915
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:52.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      2.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35105
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9920
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.58
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    4.75
 p-value of test no 39                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    3.46
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.94
 p-value of test no 46                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.84
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.53
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.43
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.74
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.50
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.05
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.83
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.07
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.51e-4
 p-value of test no 63                 :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.58
 p-value of test no 65                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.00
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.90
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5160.10
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46132
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907738
   j =  2                              :            46128
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.50
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.35
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.29
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.71
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.08
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.41
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.91
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.96
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.97
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.98
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.40
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.56
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.73
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.15
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.64
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.28
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.41
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.27
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.92
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.14
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.93
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.14
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.69
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.13
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.18
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.97
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.73
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.33
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.49
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.12
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.15
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.16
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.37
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.49
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.07
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.56
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.54
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.35
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.97
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.06
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10284.15
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.16
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.16
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.68
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.41
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.12
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.16
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.91
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999954308
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000008857
 
 Normal statistic for number of bits   :   0.070
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.090
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:19.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35106
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 4                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.33
 p-value of test no 29                 :  6.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.42
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.67
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.45
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.13
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.85
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.36
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.59
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.27
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.08
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.92
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.21
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.68
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.79
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.22
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.24
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46255
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870255
   j =  1                              :        399907493
   j =  2                              :            46249
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908795
   j =  2                              :            45592
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.06
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.78
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   65.23
 p-value of test no 123                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.82
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.04
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.38
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.13
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.96
 p-value of test no 134                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.10
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17534.57
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.14
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.58
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.04
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.47
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.92
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   64.36
 p-value of test no 151                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.22
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.89
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.08
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.26
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.65
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.29
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.86
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.08
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.28
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  414.66
 p-value of test no 163                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.76
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.21
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.59
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.21
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.10
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  304.08
 p-value of test no 169                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.14
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.48
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.58
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4782.38
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.27
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.75
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.20
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.63
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.40
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.06
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.23
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.58
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.69
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.46
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.51
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.78
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.29
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.99
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.17
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.93
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999919901
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.38
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000038362
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35107
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9904
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.55
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.21
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.21
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.29
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.26
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.53
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.22
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.07
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.64
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.48
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.72
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908326
   j =  2                              :            45834
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908337
   j =  2                              :            45824
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-5
 p-value of test no 112                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.41
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.29
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.67
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.40
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.75
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.31
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.87
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.25
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.25
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.87
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17411.53
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.81
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.63
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.89
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.76
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.22
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.25
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.01
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.53
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.05
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.76
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.13
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.87
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.95
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.05
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.42
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.81
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4838.48
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.10
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.68
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.41
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.88
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.64
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.73
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.65
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.03
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.99
 p-value of test no 179                :    0.9986
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 182                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.05
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.19
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.78
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.07
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.64
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.87
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.04
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.58
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.84
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.08
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.32
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.08
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.23
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000127330
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.37
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000037084
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.90
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35108
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4170
 p-value of test no 16                 :    0.9944
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.25
 p-value of test no 23                 :  7.8e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.85
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.95
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.30
 p-value of test no 53                 :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.47
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.69
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.50
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.77
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.10
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.60
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.63
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.02
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907647
   j =  2                              :            46175
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908502
   j =  2                              :            45749
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.58
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.26
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.26
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.59
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.32
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.31
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 127                :    0.9906
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.01
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.30
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 143                :    0.9911
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17161.87
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.95
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   64.28
 p-value of test no 147                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.25
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.75
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.07
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.80
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.88
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.09
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.09
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.74
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.70
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.04
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.95
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.55
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.87
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.00
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.52
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.27
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.42
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.58
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.41
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.74
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.61
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.11
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.99
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.02
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.45
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.35
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.03
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.45
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10321.89
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.80
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.85
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.75
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.91
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.80
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.19
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.15
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999933227
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.77
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000075271
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.028
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35109
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1224
 p-value of test no 10                 : 1 -  6.0e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334344
   j =  1                              :        599997552
   j =  2                              :             1224
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.72
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.11
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.31
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.70
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.19
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.47
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.72
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.75
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7152.46
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.68
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.73
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.88
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.68
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908265
   j =  2                              :            45866
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46251
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907500
   j =  2                              :            46247
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.05
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.34
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.40
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.32
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.60
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.52
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.13
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 131                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.20
 p-value of test no 132                :  2.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   73.64
 p-value of test no 133                :  9.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.61
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17566.61
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.00
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.38
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.97
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.67
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.96
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.21
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.02
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.24
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.37
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.50
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.83
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.15
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.67
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.98
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.21
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.21
 p-value of test no 165                :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.62
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.08
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.03
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.47
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.56
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.09
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.26
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.65
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.38
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.67
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.47
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.53
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 206                :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  260.85
 p-value of test no 207                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.02
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.08
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.83
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.88
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3922.52
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.62
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.43
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.39
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   87.32
 p-value of test no 231                :  2.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999874430
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.39
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999980537
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 238                :    0.85
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    2.53
 p-value of test no 244                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.23
 p-value of test no 254                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14          1 -  6.0e-5
  67  MatrixRank, L=30, r=26          9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35110
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 9                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.12
 p-value of test no 33                 :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.75
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.37
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.85
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.69
 p-value of test no 53                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.88
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.36
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.76
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.11
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.87
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.24
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.90
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.57
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907996
   j =  2                              :            45993
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907855
   j =  2                              :            46065
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 91                 :  2.7e-3
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 92                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.19
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.30
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.88
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.06
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.37
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.38
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.34
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.92
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.98
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.02
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.35
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17343.93
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.20
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.03
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.63
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.05
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.80
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.19
 p-value of test no 151                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.47
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.39
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.15
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.47
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.75
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.69
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.87
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.93
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.26
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.98
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.25
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.11
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.52
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.42
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.77
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.01
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.66
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.14
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.48
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.02
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.14
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.99
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.12
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.77
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.96
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.56
 p-value of test no 178                :  6.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 193                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.43
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.55
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.94
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.40
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.41
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.79
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.72
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.97
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.81
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.13
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.60
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000207142
 
 Normal statistic for number of bits   :    1.64
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.51
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999973835
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.97
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:10.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35111
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 9                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7094
 p-value of test no 19                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.07
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.32
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.82
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.18
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.66
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.24
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7256.30
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.13
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.27
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.34
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.71
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.92
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908122
   j =  2                              :            45930
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908369
   j =  2                              :            45808
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 79                 :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.11
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.39
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.08
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.02
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.60
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.40
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.00
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.24
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.83
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.97
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17416.43
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.66
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.35
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.76
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.34
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.85
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.37
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.71
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.76
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.30
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.69
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.37
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.08
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.03
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.02
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.68
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.74
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.85
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.17
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.77
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.19
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.73
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.00
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.03
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.18
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.52
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.56
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.52
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.75
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.81
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.12
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.35
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.63
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.74
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.95
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5052.04
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.97
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.33
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.06
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.94
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.25
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999989657
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.24
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999904076
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:18.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35112
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.28
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.96
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.58
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.16
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.09
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7337.22
 p-value of test no 57                 :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.35
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.41
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.26
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.49
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907827
   j =  2                              :            46082
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45784
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869784
   j =  1                              :        399908436
   j =  2                              :            45776
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.7e-3
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-6
 p-value of test no 110                :    0.9979
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.00
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.01
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.18
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.19
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.06
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 130                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    4.67
 p-value of test no 132                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   69.93
 p-value of test no 133                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.31
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.95
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.62
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.90
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.23
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.56
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.32
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.03
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.14
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.78
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.15
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.36
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.82
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.02
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.34
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.78
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.56
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.24
 p-value of test no 161                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.02
 p-value of test no 162                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.89
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.23
 p-value of test no 164                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.98
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.04
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.24
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.84
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.16
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.88
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.56
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.62
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.49
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.31
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.65
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.27
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.46
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.12
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.48
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9714.68
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.29
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.65
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.96
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.63
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.11
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12233.03
 p-value of test no 230                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.35
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000098014
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.96
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999919052
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    2.54
 p-value of test no 249                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:57.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35113
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 4                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.69
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.28
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.56
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.49
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.12
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.49
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.82
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.49
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.15
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.22
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7112.95
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.44
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.21
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.84
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4983.81
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908413
   j =  2                              :            45792
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.75
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.82
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.14
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.58
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.71
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.49
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.03
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.87
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.00
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.91
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17529.60
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.14
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.49
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.77
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.95
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.08
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.75
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.42
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.08
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.41
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.34
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.39
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.09
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.49
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.32
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.35
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.62
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.45
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.06
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.11
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.51
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.38
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.68
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.72
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.95
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.17
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.39
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.72
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.41
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.48
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.80
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.34
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.49
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.35
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.59
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.37
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.03
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.10
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.84
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11619.13
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.73
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000034102
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.76
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000068512
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:13.86
 
  All tests were passed
 
 
 
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                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35114
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4182
 p-value of test no 16                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.13
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.10
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.77
 p-value of test no 49                 :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.67
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.55
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.08
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.65
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7164.30
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.82
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.30
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.23
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.03
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.76
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907615
   j =  2                              :            46182
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908028
   j =  2                              :            45986
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
 p-value of test no 87                 :    0.9970
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.70
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.25
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.68
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.12
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.37
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.71
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.98
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.10
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.77
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.41
 p-value of test no 137                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.88
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.82
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.17
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.18
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.26
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.44
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.65
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.92
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.34
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.12
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.40
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.06
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.89
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.93
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.58
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.92
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.87
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.86
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.49
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.46
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.20
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.08
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.00
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.25
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.54
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.18
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.42
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.85
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.39
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.34
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.53
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.50
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.03
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.90
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.01
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.73
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.57
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.99
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11618.80
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.42
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.93
 p-value of test no 231                :    0.9951
 
 
 -----------------------------------------------
 Total number of bits:  7999981632
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.65
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999994568
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.074
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35115
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 9                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 11                 :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.04
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.56
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.31
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.81
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.03
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.58
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.40
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.28
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.01
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.95
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.40
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.98
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.83
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.05
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907821
   j =  2                              :            46085
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.65
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.29
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.36
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.95
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.07
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.21
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.45
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.62
 p-value of test no 136                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.83
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17100.61
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.67
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.53
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.24
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.33
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.59
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.23
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.76
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.51
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.30
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.66
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.69
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.83
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.96
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.04
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.35
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.10
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.55
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.13
 p-value of test no 167                :  7.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.77
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.57
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.90
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.66
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.37
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.06
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.30
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.80
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.05
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 180                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.26
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.84
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.47
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.53
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.13
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.58
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.19
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.90
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.75
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.89
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11591.76
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.26
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999967640
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.72
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000106594
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    2.50
 p-value of test no 244                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:46.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35116
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.80
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.84
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.86
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.14
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.76
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  494.94
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1523.45
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.38
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.38
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.89
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.29
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.22
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908365
   j =  2                              :            45813
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45419
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869419
   j =  1                              :        399909166
   j =  2                              :            45411
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  105.30
 p-value of test no 119                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.85
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.99
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.43
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.54
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.32
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.41
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.25
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.79
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.50
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17186.06
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.30
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.18
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.81
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.14
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.90
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.85
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.43
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.05
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.20
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.90
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.14
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.72
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.04
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.27
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.48
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.93
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.79
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.45
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.13
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.77
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.40
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.64
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.46
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.83
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.00
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.13
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.59
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    2.12
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.12
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.51
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.00
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.51
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.67
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.73
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.90
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.97
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.62
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.00
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.31
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.84
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999923858
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.22
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999993356
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:49.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35117
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.86
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.29
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.23
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.04
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.71
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.88
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.58
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.03
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.66
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.40
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4982.88
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908631
   j =  2                              :            45677
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45772
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869772
   j =  1                              :        399908458
   j =  2                              :            45768
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 76                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 78                 :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 102                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.21
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.37
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.04
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.32
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.59
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.98
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.37
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.54
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.089
 p-value of test no 135                :    0.9931
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-4
 p-value of test no 138                :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  178.55
 p-value of test no 141                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.52
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.92
 p-value of test no 146                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.65
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.64
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.47
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.53
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.22
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.26
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.81
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.99
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.41
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.69
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.00
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.47
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.42
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.83
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.81
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.07
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.01
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.31
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.41
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.99
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.69
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.96
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.52
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.72
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.84
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.85
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.21
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.34
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.21
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.06
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.32
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.07
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.51
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.76
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.64
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.19
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11544.37
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.73
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999868397
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.59
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999983852
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:33.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35118
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.32
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.83
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.45
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.34
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.04
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.01
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.76
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.19
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.20
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.47
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.17
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.86
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.92
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.99
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.31
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46126
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907751
   j =  2                              :            46120
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907880
   j =  2                              :            46057
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.52
 p-value of test no 119                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.27
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.71
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.03
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.70
 p-value of test no 124                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.49
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.94
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.14
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.11
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17648.18
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.80
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.56
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.02
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.61
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.07
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.25
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.74
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.29
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.37
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.54
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.42
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.97
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.78
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.84
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.21
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.90
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.64
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.49
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.52
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.29
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.93
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.48
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.64
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.30
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.40
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.82
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.25
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 200                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.25
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.81
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.38
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.03
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.76
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.39
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.74
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.77
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.67
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.35
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.59
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999890483
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999984065
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35119
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    3.30
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.23
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.58
 p-value of test no 48                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.79
 p-value of test no 49                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.57
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.17
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.25
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.22
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.47
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.14
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.42
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.96
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.46
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.68
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.80
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.22
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46402
 p-value of test no 70                 :  7.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870402
   j =  1                              :        399907204
   j =  2                              :            46386
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45469
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869469
   j =  1                              :        399909063
   j =  2                              :            45467
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-4
 p-value of test no 101                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.68
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.44
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.01
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.49
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.50
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.51
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.70
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.86
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.42
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.72
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.62
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.56
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.47
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.35
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.42
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.86
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.45
 p-value of test no 152                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.64
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.63
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.98
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.23
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.00
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.09
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.01
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  418.79
 p-value of test no 163                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.93
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.59
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.08
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.28
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.94
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.27
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.44
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.04
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  301.04
 p-value of test no 172                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.22
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.75
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.80
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.21
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.56
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 201                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    4.93
 p-value of test no 202                :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  260.47
 p-value of test no 203                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.66
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.32
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.51
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.28
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.21
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.17
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.86
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.29
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.90
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.23
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000028180
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.80
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000073912
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 243                :    0.9901
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:19.69
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35120
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 19                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.97
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.51
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.35
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.77
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.88
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.76
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.46
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.74
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.19
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.75
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.28
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907701
   j =  2                              :            46142
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908264
   j =  2                              :            45865
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.56
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.43
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.61
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.09
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.15
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.90
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.33
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.11
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.29
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17096.44
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.90
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.79
 p-value of test no 147                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.13
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.82
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.01
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.74
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.24
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.22
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.20
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.27
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.85
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.91
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.51
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.47
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.76
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.77
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  465.17
 p-value of test no 166                :  2.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.28
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.92
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.08
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.77
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.50
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.26
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.41
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.20
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.51
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.45
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.07
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.77
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.21
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.97
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.31
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.32
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
 p-value of test no 223                :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5083.27
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.75
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.83
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.76
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.92
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.57
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000015895
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.02
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000083854
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 240                :  3.5e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    7.86
 p-value of test no 242                :  1.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.49
 p-value of test no 243                :    0.9998    *****
 
 Sample variance                       :    0.23
 p-value of test no 244                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    2.41
 p-value of test no 249                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:55.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  104  AutoCor, d=3, r=0               0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35121
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.77
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    8.56
 p-value of test no 28                 :  6.8e-5    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.56
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.22
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.90
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.56
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.06
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.26
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.95
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.24
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.98
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6888.63
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.50
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.99
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.50
 p-value of test no 66                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.59
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.39
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907877
   j =  2                              :            46057
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908444
   j =  2                              :            45772
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 95                 :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.19
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.14
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.13
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.92
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.74
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.87
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.85
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.09
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17151.58
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.56
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.02
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.31
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.36
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.70
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.11
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.21
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.42
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.56
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.63
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.56
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.81
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.90
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.65
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.07
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.66
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.20
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.46
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.16
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.15
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.41
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.82
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.19
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.89
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.99
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.00
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.49
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.01
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.21
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.91
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.00
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.61
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.87
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.02
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.57
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.05
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.86
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.73
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.51
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.17
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.55
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000068701
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.11
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999969032
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    2.46
 p-value of test no 244                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.030
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:51.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            6.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35122
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4150
 p-value of test no 14                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.27
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.82
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.14
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.01
 p-value of test no 51                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.40
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.54
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.84
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.07
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.76
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.12
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.49
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.27
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.22
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.91
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908373
   j =  2                              :            45809
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908798
   j =  2                              :            45598
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.42
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.69
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.31
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.07
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.47
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.04
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.01
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.42
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17364.97
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.07
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.07
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.55
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.22
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.84
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.68
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.87
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.52
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.65
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.50
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.90
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.42
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.90
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.03
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.53
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.97
 p-value of test no 166                :  8.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.71
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.04
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.14
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.13
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.99
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.02
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.06
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.21
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.35
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.06
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.60
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    2.34
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.05
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.72
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.53
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.57
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.36
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.94
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 225                :    0.9925
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.12
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.05
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.94
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.33
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.09
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.33
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000110209
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.48
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000031900
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9966
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:56.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35123
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7513
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.35
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.44
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.55
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.21
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.74
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.87
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.98
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.73
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.89
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.95
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5171.93
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908653
   j =  2                              :            45669
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907936
   j =  2                              :            46026
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.93
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.76
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.65
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.92
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.02
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.40
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.34
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.80
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17800.87
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.11
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.44
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.24
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.31
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.45
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.84
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.12
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.32
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.70
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.67
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.22
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.85
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.96
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.66
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.09
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.51
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.96
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.94
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.12
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5170.85
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.71
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.69
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.69
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.81
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.02
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.63
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.74
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.85
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.82
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.08
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.14
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.31
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.87
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.17
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.02
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.07
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.23
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.07
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.36
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999862799
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.97
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999853202
 
 Normal statistic for number of bits   :   -1.16
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:29.48
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35124
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 11                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7508
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.35
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.09
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.14
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.62
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.84
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.01
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.12
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.25
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.80
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.90
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.32
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908757
   j =  2                              :            45611
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908424
   j =  2                              :            45776
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.84
 p-value of test no 119                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.41
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.54
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.68
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.17
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.13
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.77
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.27
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17478.97
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.77
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.06
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.35
 p-value of test no 148                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.63
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.29
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.23
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.02
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.46
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.24
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.64
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.10
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.13
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.22
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.65
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.19
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.01
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.76
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.28
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.52
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.45
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.88
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.95
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.38
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.71
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.03
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.55
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.35
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.01
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.36
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.30
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.62
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.64
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.97
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.28
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.12
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.59
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.35
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.37
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.54
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000054016
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.06
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000091939
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:22.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35125
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9938
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.63
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.68
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.26
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.71
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.57
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.69
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.48
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.96
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.04
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.09
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.59
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.83
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.06
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5250.95
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45618
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869618
   j =  1                              :        399908770
   j =  2                              :            45606
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908286
   j =  2                              :            45851
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.17
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.33
 p-value of test no 121                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.54
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.72
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.82
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.56
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.08
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.72
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.95
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.96
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.10
 p-value of test no 147                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.05
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.69
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.47
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.81
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.49
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.38
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.28
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.91
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.32
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.94
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.77
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.48
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.98
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.37
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.50
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.17
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.77
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.41
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.42
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.37
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.59
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.63
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.44
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.98
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.16
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.66
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.18
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.59
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.46
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10278.80
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.96
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.26
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.97
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.98
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4314.39
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.70
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.29
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.98
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000005386
 
 Normal statistic for number of bits   :   0.043
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.01
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000069364
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.79
 
 Sample variance                       :    2.41
 p-value of test no 244                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9930
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:33.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35126
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    4.67
 p-value of test no 27                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.98
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.67
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.61
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.00
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.36
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.58
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.06
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.62
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.01
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.84
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.73
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.81
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5109.58
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908590
   j =  2                              :            45702
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907586
   j =  2                              :            46204
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.42
 p-value of test no 117                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.32e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.94
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.00
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.87
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.50
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.68
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.87
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.92
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.27
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.01
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.09
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.55
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.79
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.06
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.34
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.91
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.17
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.20
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.58
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.44
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.40
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.77
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.13
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.75
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.08
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.57
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.72
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.91
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.12
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.42
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.22
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.44
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.39
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.10
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.44
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.40
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.07
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.61
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.40
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.43
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.08
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.95
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.71
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.87
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.73
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.01
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3961.56
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.52
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.05
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.26
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.09
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999952313
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.98
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000111385
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:31.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35127
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997337
   j =  2                              :             1330
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 12                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    4.79
 p-value of test no 38                 :  3.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.74
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.40
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.17
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.08
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.98
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.39
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.85
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.86
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.67
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.89
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.12
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.82
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.64
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.68
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.52
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.92
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.48
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908256
   j =  2                              :            45869
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908699
   j =  2                              :            45649
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.67
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.87
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.28
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.28
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.74
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.25
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.43
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.48
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17695.15
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.19
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.05
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.15
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.70
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.33
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.89
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.77
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.01
 p-value of test no 157                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.62
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.12
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.38
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.99
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.01
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.61
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.17
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.05
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.50
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.56
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.30
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.57
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.42
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.88
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.33
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.97
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.44
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.76
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.46
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.09
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.60
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.92
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.96
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.94
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5061.68
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.73
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.49
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.80
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.59
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.77
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000034522
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.77
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000005509
 
 Normal statistic for number of bits   :   0.044
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:49.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35128
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.30
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.54
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.98
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.77
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.14
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.79
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.92
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.56
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.53
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.37
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.50
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.52
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.57
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.23
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.60
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907943
   j =  2                              :            46024
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45702
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869702
   j =  1                              :        399908597
   j =  2                              :            45700
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-5
 p-value of test no 109                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.49
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.58
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.26
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.17
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.38
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.41
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.86
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.78
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.89
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9972
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.52
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.14
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.95
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.87
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.53
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.54
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.47
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.37
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.93
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.57
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.84
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.35
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.59
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.43
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.88
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.62
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.15
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.63
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.08
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.37
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5145.48
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.95
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.36
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.11
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.41
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.73
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.58
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  251.11
 p-value of test no 175                :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.75
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.88
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 188                :    0.93
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.13
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.26
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.86
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.75
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.65
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.78
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.51
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.68
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.31
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.08
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.16
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999973031
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.55
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999903599
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 246                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:16.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35129
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    3.03
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.10
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.02
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.25
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.12
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.49
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.71
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.53
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.64
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.16
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.98
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.07
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.63
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.15
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.38
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907961
   j =  2                              :            46015
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908072
   j =  2                              :            45961
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 77                 :  2.4e-3
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 78                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
 p-value of test no 90                 :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.31
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.34
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.95
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.31
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.36
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.99
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.96
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.05
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.46
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.20
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.95
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17699.10
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.37
 p-value of test no 147                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.64
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.85
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.73
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.94
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.63
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.16
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.96
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.03
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.79
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.66
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.66
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.49
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.44
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.16
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.83
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.51
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.37
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.19
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.86
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.10
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.31
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.83
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.50
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.60
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.95
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.48
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    2.24
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.10
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.17
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.39
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.60
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.29
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.62
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.13
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.80
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4311.55
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.03
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.04
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.06
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999805127
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.75
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999967604
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:29.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35130
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.30
 p-value of test no 22                 :  6.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.78
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.35
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.85
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.77
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.33
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.47
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6848.45
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.04
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.92
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.53
 p-value of test no 66                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.77
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.06
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908577
   j =  2                              :            45707
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908816
   j =  2                              :            45586
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.14
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.98
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.13
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.34
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.14
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.04
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.31
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.57
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17188.97
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.59
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.48
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.72
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.17
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.43
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.34
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.49
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.50
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.82
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.91
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.60
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.18
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.22
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.66
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.75
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.19
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.73
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.75
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.96
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.12
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.97
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.04
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.81
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.19
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.39
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.42
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.15
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.098
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.48
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.19
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.50
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.10
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.75
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.60
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.92
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.39
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.94
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.83
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.53
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000049819
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.42
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999985898
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:03.82
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35131
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7498
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     830
 p-value of test no 25                 :    0.9904
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.33
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.73
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.13
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.59
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.85
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.53
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.42
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.00
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7299.41
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.20
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.43
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.90
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.40
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.95
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45420
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869420
   j =  1                              :        399909163
   j =  2                              :            45414
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908072
   j =  2                              :            45958
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.22
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.50
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.13
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.81
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.90
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.18
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.19
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.34
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.47
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.59
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.02
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.59
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.00
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.71
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.90
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.90
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.43
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.66
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.42
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.74
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.93
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.08
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.78
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.43
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.48
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.33
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.26
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.32
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.28
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.41
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.56
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.68
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.79
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.35
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.13
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.69
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.12
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.84
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.93
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.82
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.17
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.20
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.50
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.02
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.68
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.47
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5067.09
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.90
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.58
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.19
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.39
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.93
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000013312
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.85
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999837989
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.68
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35132
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5301
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 32                 :    0.9966
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.33
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.83
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.81
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.12
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.19
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1369.90
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.73
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.47
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.34
 p-value of test no 65                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.75
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.97
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.44
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908028
   j =  2                              :            45983
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908571
   j =  2                              :            45713
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.20
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.29
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.74
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.71
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.52
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.12
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.12
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17754.49
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.81
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.88
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.66
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.80
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.98
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.75
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.77
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.04
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.25
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.23
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.98
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.71
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.52
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.10
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.29
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.43
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.70
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.42
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.51
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.09
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.32
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.17
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.32
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.24
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.79
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.47
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.92
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.23
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.49
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 202                :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.94
 p-value of test no 203                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.27
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.37
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.85
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.75
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.41
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.36
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.57
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12034.90
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.18
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.14
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999923429
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.15
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999946598
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 248                :    0.9902
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:25.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35133
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.32
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.45
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.45
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.38
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.83
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.74
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.64
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.67
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.35
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.13
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.22
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.00
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.47
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.71
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908274
   j =  2                              :            45860
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907869
   j =  2                              :            46061
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 79                 :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  4.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.92e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.48
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.00
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.63
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.98
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.80
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.00
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.34
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.65
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17666.94
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.95
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.37
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.74
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.15
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.10
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.23
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.33
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.58
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.14
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.98
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.78
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.07
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.40
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.66
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.31
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.39
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.95
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.26
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.95
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.62
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.17
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.25
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.49
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.50
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.68
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.57
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.57
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 180                :  8.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.13
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.28
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.87
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9805.43
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.24
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.77
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.23
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.08
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.64
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.65
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.41
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999965399
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.57
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999785894
 
 Normal statistic for number of bits   :   -1.69
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:21.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35134
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    3.55
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.88
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.58
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.32
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.80
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.69
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.10
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.98
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.84
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.40
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.50
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.84
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.68
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45421
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869421
   j =  1                              :        399909159
   j =  2                              :            45419
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908245
   j =  2                              :            45870
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
 p-value of test no 93                 :    0.9981
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.45e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.20
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.32
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.45
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.98
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.95
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.55
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.24
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 130                :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    5.42
 p-value of test no 132                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   17.19
 p-value of test no 133                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.82
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.89
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.19
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.88
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.85
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.89
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.98
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.58
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.13
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.23
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.07
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.02
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.00
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.99
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.47
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.53
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.42
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.52
 p-value of test no 162                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.65
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.91
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.08
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.73
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.10
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.46
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.74
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.40
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.45
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.95
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.11
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.95
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.55
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.47
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.83
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.17
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.55
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 206                :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.54
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.88
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.40
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.45
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.18
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.38
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.55
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.61
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.23
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.75
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000020107
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.65
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999882017
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9912
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    2.16
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35135
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 9                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.57
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.34
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.29
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.26
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.13
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.05
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.23
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.95
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.13
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7299.35
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.66
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.10
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.97
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.48
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46005
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870005
   j =  1                              :        399907994
   j =  2                              :            45997
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908667
   j =  2                              :            45659
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-3
 p-value of test no 83                 :    0.9976
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 92                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 103                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 105                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.03
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.85
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.21
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.93
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.55
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.29
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.17
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.03
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.62
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.34
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.86
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.48
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.47
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.31
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.98
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.81
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.44
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.55
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.28
 p-value of test no 155                :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.42
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.55
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.56
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.75
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.15
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.79
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.78
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.74
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.05
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.42
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.81
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.64
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.34
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.65
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.96
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.72
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.22
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.57
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.12
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.95
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.15
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.55
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 180                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.00
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.54
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10190.59
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.79
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.26e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.87
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.18
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.38
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.06
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.10
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.94
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.71
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999974471
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.51
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000028042
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:27.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35136
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.49
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.12
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.96
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.61
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.50
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.43
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.46
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.91
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.90
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.41
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.18
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.08
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908653
   j =  2                              :            45669
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907612
   j =  2                              :            46191
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
 p-value of test no 100                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.88
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.17
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.49
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.08
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.26
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.49
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.66
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.93
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.12
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17712.49
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.40
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.93
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.47
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.28
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.33
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.65
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.23
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.05
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.35
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.06
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.96
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.19
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.26
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.23
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.41
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.10
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.58
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.72
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.91
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.73
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.85
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.66
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.78
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.56
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.41
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.30
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.89
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.36
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.15
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.59
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.23
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.44
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.95
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 214                :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9648.00
 p-value of test no 215                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.039
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.77
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.21
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.93
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.68
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.24
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.22
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.36
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000038569
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.55
 p-value of test no 233                :  6.1e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000118579
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.77
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:36.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35137
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 10                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.19
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.26
 p-value of test no 49                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.03
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.31
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.23
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.07
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.19
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.54
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.32
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.15
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.58
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.99
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.44
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46132
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907737
   j =  2                              :            46130
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908459
   j =  2                              :            45769
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.30
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.71
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.57
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.13
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.22
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.38
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.41
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17706.45
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.95
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.19
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.91
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.15
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.13
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.59
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.44
 p-value of test no 155                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.94
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.54
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.43
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.32
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.78
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.09
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.98
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.38
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.96
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.69
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.74
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.28
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.61
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.61
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.70
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.77
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.22
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.21
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.65
 p-value of test no 207                :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9954
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.34
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.03
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.65
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.37
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3916.14
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.72
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.49
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12241.04
 p-value of test no 230                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.97
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000027865
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.00
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000048928
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:30.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35138
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7122
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.34
 p-value of test no 35                 :  6.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.96
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.84
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.33
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.68
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.21
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.14
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.90
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.11
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.52
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5041.54
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908234
   j =  2                              :            45877
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908023
   j =  2                              :            45981
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-4
 p-value of test no 86                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.77
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.52
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.13
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.78
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.62
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.33
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.86
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.17
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.87
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17326.63
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.97
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.18
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.75
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.86
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.21
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.75
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.80
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.85
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.05
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.14
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.97
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.12
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.59
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.85
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.38
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.49
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.63
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.13
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.25
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.85
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.48
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.10
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4828.85
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.97
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.39
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.84
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.31
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.33
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.43
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.12
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.61
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.42
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.71
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.97
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.07
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.79
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.15
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000130273
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.10
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999923849
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.085
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:29.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35139
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     251
 p-value of test no 37                 :    0.9980
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.97
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.97
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.11
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.10
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.88
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.69
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.24
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.97
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.24
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7274.23
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.55
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.50
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.77
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.97
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.07
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908549
   j =  2                              :            45724
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46296
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870296
   j =  1                              :        399907413
   j =  2                              :            46286
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9973
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-4
 p-value of test no 112                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-5
 p-value of test no 113                :    0.9953
 
 Anderson-Darling statistic = A2       :    5.16
 p-value of test no 114                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.87
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.56
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.63
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.90
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.17
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.01
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.31
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.51
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.01
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.31
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.44
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.99
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.73
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.59
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.27
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.43
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.06
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.35
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.65
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.12
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.51
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.66
 p-value of test no 159                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.13
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.59
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.64
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.62
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.37
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.72
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.11
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.94
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.79
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.10
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.92
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.90
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.90
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.06
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.47
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.29
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.19
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.71
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.99
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.98
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.95
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.59
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.78
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.29
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.71
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.76
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.29
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.50
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.30
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999921557
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.95
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000037735
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:27.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35140
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5364
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.53
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.31
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.79
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.15
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.64
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.27
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7148.46
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.29
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.93
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.93
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.82
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.24
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908215
   j =  2                              :            45882
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907911
   j =  2                              :            46043
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 84                 :    0.9906
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-4
 p-value of test no 94                 :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9957
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.22
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.69
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.18
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.80
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.69
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-5
 p-value of test no 127                : 1 -  6.0e-5    *****
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 128                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.51
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.87
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  7.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.10
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17774.35
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.12
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.41
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.78
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.24
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.73
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.87
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.53
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.54
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.71
 p-value of test no 156                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.68
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.65
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.06
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.42
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.75
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.88
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.33
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.67
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.31
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.29
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.36
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.28
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.35
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.27
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.32
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.09
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.32
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.51
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.69
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.98
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.45
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.14
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.84
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.43
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.36
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.86
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.27
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.97
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.42
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.10
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.14
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.85
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000042259
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.46
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999932678
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.22
 p-value of test no 244                :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 246                :    0.9934
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 247                :  7.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.83
 p-value of test no 248                :    0.9976
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:04.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35141
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997359
   j =  2                              :             1319
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    2.67
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    3.96
 p-value of test no 39                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.14
 p-value of test no 46                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.46
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.86
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.89
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.64
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.25
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.67
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.42
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.64
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.10
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.62
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.85
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907571
   j =  2                              :            46213
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46377
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870377
   j =  1                              :        399907252
   j =  2                              :            46365
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.62
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.14
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.55
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.17
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.54
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.99
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.97
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.45
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.21
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.02
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17172.49
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.06
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.62
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.15
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.17
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.97
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.46
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.39
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.57
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.00
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.47
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.79
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.39
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.56
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.32
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.90
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.93
 p-value of test no 162                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.15
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.55
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.49
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.29
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.16
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.42
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.64
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.41
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  462.49
 p-value of test no 172                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.92
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.18
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.44
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.22
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    2.15
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.79
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.84
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.30
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10338.26
 p-value of test no 215                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.61
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.43
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.03
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.90
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12053.80
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.19
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.84
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999972677
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.13
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999962576
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 236                :    0.9902
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:52.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35142
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1478
 p-value of test no 8                  :  1.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334598
   j =  1                              :        599997044
   j =  2                              :             1478
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4508
 p-value of test no 16                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.17
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.87
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.18
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.40
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.99
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.69
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.42
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.19
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7216.99
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.18
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.59
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.34
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.34
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.05
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907701
   j =  2                              :            46142
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45908
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869908
   j =  1                              :        399908187
   j =  2                              :            45902
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 73                 :    0.9941
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.37e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.39
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.45
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.45
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.49
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.69
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.39
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 138                :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.53
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17669.86
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.73
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.62
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.09
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.33
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.92
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.50
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.43
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.10
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.66
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.37
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.54
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.66
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.10
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.63
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.72
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.97
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.12
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.99
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.94
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.83
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.96
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.12
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.96
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.09
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.55
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.10
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.67
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.80
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.82
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.89
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9930
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.69
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.69
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.30
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.23
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3887.69
 p-value of test no 228                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.47
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.76
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.68
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999959705
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.77
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999996128
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    2.16
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.019
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:19.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35143
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.62
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.05
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.30
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.58
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.11
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.03
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.20
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.15
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.49
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.44
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4819.93
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908961
   j =  2                              :            45515
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908516
   j =  2                              :            45739
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9951
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 98                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
 p-value of test no 106                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.55
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.35
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.19
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.62
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.62
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.39
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17309.80
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.33
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.04
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.36
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.08
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.26
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.77
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.27
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.47
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.86
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.05
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.02
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.96
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.10
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.92
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.43
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.29
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.79
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.90
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.59
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.47
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.33
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.71
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.10
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.34
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.85
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.30
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.56
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.44
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.92
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.93
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.85
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.56
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.08
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.51
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.42
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.17
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.70
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.77
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.22
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.79
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11643.38
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.49
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000059953
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.58
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999916505
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:36.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35144
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4171
 p-value of test no 16                 :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.62
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.03
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.61
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.76
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.45
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.74
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7277.27
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.63
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.90
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.80
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.77
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5231.62
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908064
   j =  2                              :            45965
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908201
   j =  2                              :            45895
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 84                 :    0.9966
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 85                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.06
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.94
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.24
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.16
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.02
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.37
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.41
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.81
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.45
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.40
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.92
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.66
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.79
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.07
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.98
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.91
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.43
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.38
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.42
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.37
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.94
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.81
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.61
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.29
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.17
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.61
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.39
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.82
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.88
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.02
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.49
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.54
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.83
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.24
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.49
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.62
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.12
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.83
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10253.54
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.63
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 221                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4641.96
 p-value of test no 222                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.42
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.48
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.25
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.22
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.61
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.60
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000115069
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.02
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000128218
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:16.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35145
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.92
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.04
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.96
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.42
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.05
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.47
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.62
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1349.71
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.79
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.33
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.24
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.30
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5312.68
 p-value of test no 68                 :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908421
   j =  2                              :            45779
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45483
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869483
   j =  1                              :        399909037
   j =  2                              :            45477
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.65
 p-value of test no 116                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.58
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.00
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.43
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.05
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.25
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.14
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.98
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 132                :    0.9914
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.53
 p-value of test no 134                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
 p-value of test no 138                :    0.9904
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.18
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.64
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.44
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.67
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.21
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.78
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.85
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.48
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.33
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.39
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.85
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.80
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.37
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.78
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  567.92
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.07
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.46
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.90
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.55
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.22
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.60
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.66
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.04
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.59
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.63
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.40
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.30
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.01
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.89
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.65
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  160.96
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.65
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.57
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.99
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.52
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.74
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.80
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.16
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.48
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.48
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.27
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3910.15
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.51
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.30
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11508.59
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.43
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000040852
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.65
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999963764
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:03.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35146
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7089
 p-value of test no 15                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.91
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     337
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.29
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.89
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.09
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.61
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.24
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.72
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.86
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.44
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.91
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.28
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.51
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.59
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.84
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908376
   j =  2                              :            45806
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908246
   j =  2                              :            45874
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.05
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.93
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.03
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.82
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.74
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.31
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.05
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.66
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.30
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.29
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.02
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.77
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.89
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.89
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.49
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.54
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.61
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.32
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.70
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.32
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.15
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.61
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.71
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.75
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.38
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.94
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.15
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.28
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.96
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.02
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.02
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.50
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.42
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.34
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.81
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.16
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.72
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.98
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.70
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.33
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.93
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.61
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.15
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.08
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.52
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.49
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.41
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.40
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.51
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.86
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.34
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.06
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000217696
 
 Normal statistic for number of bits   :    1.72
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.27
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999970781
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:15.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35147
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 38                 :    0.9914
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.22
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.51
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.15
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.26
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.00
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.27
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.95
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1351.20
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.60
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.42
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.81
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.94
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.33
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908460
   j =  2                              :            45761
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908089
   j =  2                              :            45954
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-4
 p-value of test no 76                 :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 101                :    0.9985
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.15
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.91
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.02
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.06
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.04
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.57
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17223.56
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.25
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.67
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.33
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.23
 p-value of test no 150                :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.71
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.42
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.81
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.63
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.13
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.29
 p-value of test no 158                :  8.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.70
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.55
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.10
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.22
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.41
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.05
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.45
 p-value of test no 166                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.30
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.66
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.71
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.02
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.53
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.89
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.22
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.61
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.56
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.76
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.72
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.34
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.07
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.29
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.58
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.98
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.30
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.41
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.06
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11698.92
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12239.48
 p-value of test no 230                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.76
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999865061
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.99
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999967442
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:20.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35148
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 6                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.90
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.28
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.65
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.97
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.76
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.50
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.20
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.71
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.22
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.09
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.90
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.36
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.98
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.95
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46265
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870265
   j =  1                              :        399907473
   j =  2                              :            46259
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908382
   j =  2                              :            45806
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 73                 :    0.9928
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.20
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.99
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.55
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   74.53
 p-value of test no 124                :  2.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.51
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.96
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.04
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.36
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.47
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.00
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.06
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.40
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.05
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.59
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.07
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.31
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.76
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.99
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.24
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.10
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.18
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.17
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.71
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.42
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.78
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.67
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.75
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.27
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.41
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.34
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.38
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.41
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.21
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.44
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.91
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.82
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.92
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.20
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   30.08
 p-value of test no 176                :  2.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.94
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.63
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.78
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.49
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.96
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.61
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.89
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.45
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.92
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.97
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.34
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12262.48
 p-value of test no 230                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.79
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000075526
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.35
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999919256
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.73
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  64  WeightDistrib, r = 26           2.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35149
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9938
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.63
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.33
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.06
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.89
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.42
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.64
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.64
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1366.42
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.26
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.39
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.82
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.44
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4796.61
 p-value of test no 68                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908167
   j =  2                              :            45912
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908078
   j =  2                              :            45958
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 79                 :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  4.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 86                 :  7.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 88                 :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9934
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.4e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.11
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.74
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.34
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.60
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.84
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.69
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.96
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.14
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.29
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.55
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.39
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.81
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.90
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.25
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.10
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.82
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.50
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.05
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.04
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.46
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.88
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.16
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.58
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.94
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.78
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.44
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.24
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.60
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.17
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.20
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.67
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.17
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.23
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.20
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.06
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.28
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.85
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.91
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.73
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.73
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.02
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.59
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.22
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.11
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.78
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10311.67
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.83
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.72
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.49
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3918.76
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.28
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.52
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.26
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000004294
 
 Normal statistic for number of bits   :   0.034
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.79
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000114952
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    2.75
 p-value of test no 244                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35150
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     981
 p-value of test no 25                 :  4.0e-3
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.82
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9915
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.42
 p-value of test no 47                 :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.88
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.22
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.27
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.69
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.62
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.06
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  517.06
 p-value of test no 55                 :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.86
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.62
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.58
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.38
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.97
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.56
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908720
   j =  2                              :            45637
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  8.9e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -7.38e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.11
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.69
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.64
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.36
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.41
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.58
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17649.65
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.22
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.10
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.48
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.20
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.72
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.30
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.97
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.75
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.53
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.76
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.38
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.62
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.10
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.24
 p-value of test no 161                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.54
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.84
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.99
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.71
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.71
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.08
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.08
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.08
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.03
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.05
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.88
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.33
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.11
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.56
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.44
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.59
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.80
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.24
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.78
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.88
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.44
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.71
 p-value of test no 216                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.53
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.29
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.36
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.24
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.22
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12093.05
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999821219
 
 Normal statistic for number of bits   :   -1.41
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.66
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000094570
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 243                :    0.26
 
 Sample variance                       :    2.44
 p-value of test no 244                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35151
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.2e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9967
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.51
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.72
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.50
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.78
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.56
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.61
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.59
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.85
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.69
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6880.20
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.60
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.76
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.18
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.83
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908313
   j =  2                              :            45839
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46249
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870249
   j =  1                              :        399907503
   j =  2                              :            46247
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.98
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.99
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.94
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.21
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.36
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.14
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.54
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.97
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 142                :  9.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    6.42
 p-value of test no 144                :  6.7e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16885.54
 p-value of test no 145                :    0.9984
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.94
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.19
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.94
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.53
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.12
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.13
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.53
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.43
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.24
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.10
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.71
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.47
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.08
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.43
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.63
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.29
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.01
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.78
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.74
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.47
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.79
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.06
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.59
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.12
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.91
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.80
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.79
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.49
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.12
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.15
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.71
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-3
 p-value of test no 191                :    0.98
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 194                :  2.8e-3
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 195                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.88
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.82
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.76
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.48
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.29
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.37
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.72
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.51
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.03
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11762.60
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.63
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999924905
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.26
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999958493
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.036
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               2.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35152
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 11                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.30
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.52
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.18
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.63
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.84
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.26
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.92
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.10
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.77
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.64
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7230.45
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.75
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.72
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.12
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.21
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.22
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908518
   j =  2                              :            45735
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45513
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869513
   j =  1                              :        399908978
   j =  2                              :            45505
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.87
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.51
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.14
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.43
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.24
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.66
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.00
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.83
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.26
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.05
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.80
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.53
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.59
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.81
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.59
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.23
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.69
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.43
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.34
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.50
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.76
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.91
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.87
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.20
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.12
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.52
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.12
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.67
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.74
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.25
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.90
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.02
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.93
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.23
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.70
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.09
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.75
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.91
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.51
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.94
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.97
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.26
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9790.75
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.69
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.18
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.72
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.55
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.34
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.80
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.94
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.60
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000118195
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000140665
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    2.42
 p-value of test no 239                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35153
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 11                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5242
 p-value of test no 13                 :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    4.88
 p-value of test no 39                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.19
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.88
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.29
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.29
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.10
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.45
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7084.69
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.28
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.29
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.72
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.04
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908812
   j =  2                              :            45588
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907960
   j =  2                              :            46017
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.19
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.10
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.09
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.82
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.95
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 127                :    0.9938
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.10
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.91
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.43
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.41
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.82
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.07
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.49
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.93
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.57
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.70
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.38
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.07
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.49
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.35
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.53
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.71
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.55
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.22
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.86
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.08
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.16
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.59
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.31
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.27
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.33
 p-value of test no 170                :    0.9940
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.94
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.58
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.60
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.66
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.36
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.84
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 182                :    0.9975
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.52
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.94
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.56
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.05
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.87
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.84
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.29
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.77
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11570.01
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.44
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.22
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000084220
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.51
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999966776
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    2.43
 p-value of test no 239                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:18.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35154
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     951
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9935
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.74
 p-value of test no 48                 :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.29
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.05
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.78
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.99
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.61
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.62
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7202.52
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.14
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.44
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.21
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.89
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.56
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45587
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869587
   j =  1                              :        399908831
   j =  2                              :            45577
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908418
   j =  2                              :            45791
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.50
 p-value of test no 117                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.54
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.69
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.30
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.92
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.02
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.15
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.70
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.12
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17386.92
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.11
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.32
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.41
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.91
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.67
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.53
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.62
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.59
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.37
 p-value of test no 155                :    0.9904
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.56
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.91
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.52
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.70
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.75
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.83
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.19
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.56
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.57
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.12
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.93
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.15
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.80
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.42
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.33
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.61
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.46
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.85
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.87
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 179                :  8.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.00
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.68
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.98
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.28
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.55
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.31e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.12
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.66
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.04
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.71
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.73
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.72
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.29
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999884081
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.34
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000135679
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:51.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35155
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 26                 :    0.9943
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     258
 p-value of test no 37                 :    0.9928
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.83
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.93
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.17
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.68
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.78
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.43
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.98
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.84
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.73
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.06
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.29
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45843
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869843
   j =  1                              :        399908316
   j =  2                              :            45839
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.97
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.80
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.58
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.80
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.65
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.38
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.51
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.29
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17171.12
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.13
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.68
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.33
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.24
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.67
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.11
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.10
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.73
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.65
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.92
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.47
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.75
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.84
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.37
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.75
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.56
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.47
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.76
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.77
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.04
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.55
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.95
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.75
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.22
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.70
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.81
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.71
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.75
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.56
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.22
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.07
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.27
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.34
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.40
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.11
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.17
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.25
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.01
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.87
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000039664
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.72
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999973523
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 241                :    0.9947
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:13.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35156
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 6                  :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.83
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.28
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.32
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.66
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.32
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.37
 p-value of test no 51                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.36
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.73
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.70
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.61
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.80
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.91
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.59
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.49
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.22
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.61
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907958
   j =  2                              :            46015
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46153
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907696
   j =  2                              :            46149
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.35
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.15
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.54
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.64
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.81
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.73
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.02
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.24
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.05
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.48
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.40
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.83
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.32
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.59
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.73
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.47
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.17
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.27
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.57
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.19
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.23
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.77
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.12
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.14
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.57
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.62
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.00
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.82
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.90
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.15
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5231.66
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.22
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.83
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.61
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.36
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.38
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.73
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.53
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.82
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.35
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.73
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.75
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.61
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3866.10
 p-value of test no 227                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.72
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.56
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.18
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.30
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000078784
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.78
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999985049
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 238                :    0.07
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35157
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7591
 p-value of test no 21                 :  7.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.83
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.59
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.54
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.89
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.81
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.22
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.80
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.97
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.07
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.92
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.11
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.23
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.85
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.56
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46272
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870272
   j =  1                              :        399907459
   j =  2                              :            46266
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908244
   j =  2                              :            45872
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.98
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.25
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.35
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.23
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.99
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.86
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.75
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.28
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.80
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.48
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.41
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.17
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.48
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.26
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.29
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.97
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.90
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.16
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.42
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.74
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.70
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.77
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.08
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.65
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.22
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.09
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.15
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  479.60
 p-value of test no 167                :  6.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.55
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.42
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.61
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.82
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.71
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.55
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.88
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.13
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.84
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.11
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.19
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.79
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.67
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9788.86
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10113.51
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4727.66
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.24
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.80
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.85
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.33
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.01
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.13
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999986894
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.38
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999893636
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-3
 p-value of test no 235                :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.56
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:22.72
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        7.8e-4
  78  RandomWalk1 M (L=10000, r=0)    6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35158
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.62
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.15
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.20
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.77
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.27
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.30
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.82
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.70
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.56
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.68
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.41
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.57
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.41
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.94
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.63
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45881
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869881
   j =  1                              :        399908243
   j =  2                              :            45871
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908153
   j =  2                              :            45919
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.45
 p-value of test no 115                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.30
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.29
 p-value of test no 120                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.33
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.85
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.13
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.27
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.66
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.43
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.58
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.81
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.23
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17220.82
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.78
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.12
 p-value of test no 147                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.69
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.40
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.33
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.97
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.77
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.10
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.60
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.28
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.33
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.62
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.64
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.43
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.90
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.61
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.16
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.35
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.73
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.97
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.27
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.05
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.89
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.16
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.52
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.17
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.95
 p-value of test no 187                :  9.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.54
 p-value of test no 188                :  5.5e-3
 
 Sample variance                       :    2.48
 p-value of test no 189                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.84
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.72
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.07
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.55
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.02
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.01
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 224                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 225                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5179.78
 p-value of test no 226                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.01
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.60
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12104.51
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.76
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.24
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999987659
 
 Normal statistic for number of bits   :  -0.098
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.78
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999978128
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:44.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35159
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.79
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.14
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.75
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.99
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.33
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.62
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.10
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.85
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.26
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.05
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.46
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.64
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.30
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908063
   j =  2                              :            45961
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.61
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.48
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.77
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.17
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.94
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.75
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.15
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.33
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.99
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.66
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17599.58
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.18
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.02
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.06
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.56
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.36
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.45
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.98
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.32
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.14
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.73
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.92
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.46
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.01
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.42
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.12
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.46
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.15
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.48
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.59
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.17
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.50
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.33
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4812.06
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.99
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.08
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.08
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.28
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.80
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.60
 p-value of test no 174                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.93
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.93
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.58
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.19
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.16
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.09
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.13
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.00
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.36
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.92
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.22
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.42
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.75
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000100681
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.26
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000024553
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 238                :    0.99
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:57.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35160
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.30
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.27
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.42
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.98
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.94
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.29
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.76
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.94
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.81
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.00
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.03
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.17
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.70
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4840.34
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908103
   j =  2                              :            45944
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907778
   j =  2                              :            46105
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.50e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.89
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.27
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.09
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.05
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.79
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.58
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.23
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.48
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.28
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.61
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.28
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.99
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.01
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.65
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.38
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.22
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.94
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.44
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.49
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.63
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.71
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.89
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   38.23
 p-value of test no 165                :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.17
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.89
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.13
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  445.09
 p-value of test no 169                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.05
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.09
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.94
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.32
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.10
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.21
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.54
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.44
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.31
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.83
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.58
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5071.31
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.94
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.90
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.69
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.69
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.02
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.45
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999947021
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.82
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000022630
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35161
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 5                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5273
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.70
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.38
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.46
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.55
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.42
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.73
 p-value of test no 52                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.32
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.35
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.58
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.87
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.39
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.35
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.25
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.42
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.15
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46304
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870304
   j =  1                              :        399907397
   j =  2                              :            46294
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907869
   j =  2                              :            46061
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
 p-value of test no 73                 :    0.9978
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 100                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 117                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.22
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.70
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.95
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.41
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.00
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.67
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.57
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.34
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.23
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.79
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.40
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.73
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.23
 p-value of test no 149                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.59
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.29
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.02
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.73
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.71
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.27
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.05
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.08
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.04
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.17
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.77
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.98
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.34
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.03
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.12
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.77
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.86
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.42
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.41
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5271.25
 p-value of test no 173                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.53
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.04
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.74
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.98
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.76
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.56
 p-value of test no 198                :  4.0e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.00
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.33
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.76
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.55
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.40
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.14
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.70
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.86
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.28
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.78
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.35
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999972614
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.55
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000056773
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:30.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35162
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.92
 p-value of test no 34                 :  3.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.36
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.28
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.28
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.03
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.11
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.16
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  365.99
 p-value of test no 55                 :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.73
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.88
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.62
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.97
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.96
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4876.25
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907951
   j =  2                              :            46017
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908282
   j =  2                              :            45853
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.83
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.07
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.97
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.74
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.91
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.19
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.35
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 126                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.90
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.37
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.94
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.04
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.38
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.05
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.60
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.52
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.94
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.25
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.98
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.63
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.47
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.96
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.98
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.22
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.74
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.11
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.89
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.55
 p-value of test no 165                :  9.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.85
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.46
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5149.00
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.42
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.98
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.46
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.09
 p-value of test no 172                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.44
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.82
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.35
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.09
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.13
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.97
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.42
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.07
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.61
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.04
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.86
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5137.36
 p-value of test no 226                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.68
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.52
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.95
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.28
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.23
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000068125
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.28
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000071761
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 251                :    0.9951
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:30.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35163
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 10                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 18                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.04
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.98
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.08
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.52
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.80
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.89
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.09
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-4
 p-value of test no 59                 :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.14
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.96
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.97
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.76
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.55
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908472
   j =  2                              :            45761
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45481
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869481
   j =  1                              :        399909041
   j =  2                              :            45475
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.24
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.34
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.86
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.13
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.67
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.31
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.81
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.20
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.42
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16974.73
 p-value of test no 145                :    0.9930
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.08
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.35
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.32
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.26
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.12
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.01
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.05
 p-value of test no 152                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.74
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.66
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.65
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.23
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.35
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.09
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.50
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.68
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  198.42
 p-value of test no 164                :  3.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.82
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.18
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.51
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.49
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.30
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.09
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.03
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.93
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.93
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.98
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.31
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.29
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.97
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.47
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.19
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.69
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.45
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.27
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.10
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.41
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.98
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.98
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.37
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.69
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999918776
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.94
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000125671
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
 p-value of test no 235                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:13.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35164
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7524
 p-value of test no 18                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    3.05
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.84
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.58
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.12
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.79
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.31
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.85
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.98
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7250.79
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.94
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.70
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.53
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.59
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.71
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907895
   j =  2                              :            46048
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46038
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870038
   j =  1                              :        399907928
   j =  2                              :            46030
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
 p-value of test no 91                 :    0.9979
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.49
 p-value of test no 116                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.72
 p-value of test no 118                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.54
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.61
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.41
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.33
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.61
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.35
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.02
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.82
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.85
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17260.46
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.51
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.23
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.46
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.14
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.88
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.24
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.33
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.72
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.61
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.59
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.09
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.35
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.31
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.26
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.19
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.99
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.24
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.67
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.53
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.87
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.78
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.13
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.10
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.40
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.57
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.36
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.31
 p-value of test no 175                :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.87
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.88
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.54
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.98
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.79
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.21
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.40
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.55
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.54
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.27
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11614.90
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.33
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000001444
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.93
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999940862
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:20.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35165
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 14                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.50
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9977
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.37
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.87
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.31
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.10
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.45
 p-value of test no 51                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.87
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.66
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.99
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.90
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6913.15
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.57
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.40
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.78
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.58
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46363
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870363
   j =  1                              :        399907277
   j =  2                              :            46357
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 92                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 9.18e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.036
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.01
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.82
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.15
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.28
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.22
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.72
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.97
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.11
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.01
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.95
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.91
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.70
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.89
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.49
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.75
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.46
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.77
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.46
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.13
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.98
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.13
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.63
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.04
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.48
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.77
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.11
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.95
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.52
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.64
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.45
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  257.28
 p-value of test no 170                :  3.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.60
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.89
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.77
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.09
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.98
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.50
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 204                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
 p-value of test no 205                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 206                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  140.54
 p-value of test no 207                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.35
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9703.41
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.10
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.35
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.62
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.06
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.90
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.72
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.82
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999998420
 
 Normal statistic for number of bits   :  -0.012
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.91
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000020293
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.65
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:06.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35166
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7070
 p-value of test no 21                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.39
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.82
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.24
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.54
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.74
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.68
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.79
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.54
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7279.90
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.52
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.10
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.72
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.46
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.56
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907769
   j =  2                              :            46111
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908053
   j =  2                              :            45969
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.49
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.81
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.10
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.28
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.23
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.64
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.43
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17431.97
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.72
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.04
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.45
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.36
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.74
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.26
 p-value of test no 153                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.39
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.22
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.53
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.83
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.25
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.52
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.85
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.65
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.95
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.47
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.54
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.89
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.31
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.20
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.07
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.39
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.73
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.41
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.72
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.21
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.28
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.41
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.67
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.29
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.56
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.80
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.90
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.65
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.86
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.24
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.99
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.56
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.05
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999966281
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.52
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999928139
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35167
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.95
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.68
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.22
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.05
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.79
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.81
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.55
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.93
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.72
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.03
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.73
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.31
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.65
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.38
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908045
   j =  2                              :            45976
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45430
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869430
   j =  1                              :        399909141
   j =  2                              :            45428
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.86
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  105.23
 p-value of test no 120                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.91
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.96
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.68
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.20
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 127                :    0.9940
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.27
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.07
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.29
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17403.45
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.35
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.61
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.19
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.28
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.01
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.38
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.74
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.67
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.69
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.21
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.38
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.01
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.38
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.47
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.25
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.15
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.83
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.42
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.38
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.75
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4799.92
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.53
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.04
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.17
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.09
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.34
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.71
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.87
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.26
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 182                :    0.9996    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.01
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.20
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.81
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.21
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.95
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.33
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.88
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.57
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.78
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12136.86
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.61
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000050395
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.77
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999916655
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:36.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35168
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1497
 p-value of test no 11                 :  2.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334617
   j =  1                              :        599997006
   j =  2                              :             1497
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.81
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.44
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.30
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.56
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.07
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.19
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.41
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.84
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.81
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.87
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7216.67
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.62
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.95
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.07
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.11
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.75
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907755
   j =  2                              :            46115
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908013
   j =  2                              :            45986
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.27
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.84
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.44
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.09
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.01
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.40
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.24
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.40
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.87
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.14
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.49
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.05
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.84
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.06
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.91
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.80
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.87
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.67
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.47
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.09
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.29
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.41
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.60
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.80
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.80
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.50
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.38
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.65
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.02
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.97
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.45
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.70
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.02
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.51
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.36
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.71
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.42
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.39
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.58
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.82
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.01
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.46
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.13
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.88
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.62
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.77
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.25
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.37
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.59
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.11
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.41
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999901700
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.08
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000107449
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 243                :    0.12
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:20.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35169
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 8                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 18                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7522
 p-value of test no 21                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.36
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.32
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.36
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.28
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.14
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.35
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.51
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6977.77
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.94
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.87
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.47
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.11
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.41
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908242
   j =  2                              :            45876
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45486
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869486
   j =  1                              :        399909033
   j =  2                              :            45476
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 91                 :    0.9928
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.66
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.18
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.89
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.45
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.96
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.08
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.28
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 142                :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
 p-value of test no 143                :    0.9977
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16968.12
 p-value of test no 145                :    0.9937
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.25
 p-value of test no 146                :    0.9965
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.19
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.51
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.09
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.18
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.28
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.00
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.58
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.62
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.58
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.97
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.94
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.87
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.07
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.19
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.83
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.48
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.05
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.16
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.88
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.18
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.85
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.06
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.92
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.48
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.09
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.56
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  5.5e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.62
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.23
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.59
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10330.54
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9714.18
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.64
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.63
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.57
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.02
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.23
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.96
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.69
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000080101
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.68
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999942743
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 237                :    0.9986
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    2.33
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:54.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35170
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9910
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.15
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.89
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.44
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.88
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.65
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.05
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.70
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.86
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 63                 :    0.9913
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   36.72
 p-value of test no 65                 :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.90
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.15
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.37
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908589
   j =  2                              :            45698
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908465
   j =  2                              :            45760
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 78                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.60
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.59
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.55
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.58
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.70
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.96
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.43
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.52
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.44
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.74
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.03
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.62
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.41
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.31
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.17
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.33
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.39
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.69
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.23
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.11
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.38
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.88
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.65
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.54
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.90
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.73
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.47
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.00
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.25
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.56
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.63
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.13
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.17
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.84
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.07
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.80
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.94
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.71
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.65
 p-value of test no 196                :  3.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.89
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.40
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.91
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.66
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 212                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9679.46
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.86
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.37
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.85
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.07
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12139.69
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.97
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.33
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999924551
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.74
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000079570
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:03.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35171
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 10                 :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5305
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.83
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.42
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.45
 p-value of test no 51                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.01
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.02
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.71
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.46
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.42
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7210.11
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.72
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.20
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.85
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.37
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.13
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907605
   j =  2                              :            46193
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907935
   j =  2                              :            46028
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.99
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.28
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.52
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.15
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.13
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.73
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.19
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.75
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.10
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.46
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.15
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.71
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.30
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.00
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.88
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.40
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.32
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.75
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.07
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.92
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.39
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.61
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.82
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.58
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.56
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.11
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.11
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.43
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.26
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.43
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.37
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.07
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.55
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    2.79
 p-value of test no 184                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9930
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.47
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.48
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.41
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.72
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.07
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.37
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.69
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.66
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.07
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4342.53
 p-value of test no 228                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.45
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.55
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.93
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000119203
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.38
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000129025
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.25
 p-value of test no 249                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:02.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35172
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1514
 p-value of test no 11                 :  3.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334634
   j =  1                              :        599996972
   j =  2                              :             1514
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5567
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.32
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.71
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.63
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.91
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.64
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1560.24
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.84
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 58                 :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 60                 :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.42
 p-value of test no 61                 :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.27
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.07
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.38
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.55
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908494
   j =  2                              :            45744
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.97
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.34
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.57
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.80
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.16
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.10
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.24
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.33
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 131                :    0.9944
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.73
 p-value of test no 133                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.73
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.22
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.54
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.16
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.47
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.78
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.30
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.23
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.05
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.04
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.88
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.11
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.91
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.56
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.87
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.91
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.63
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.48
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.85
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.89
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.25
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.13
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.17
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.65
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.47
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.68
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.54
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.46
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.08
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.81
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.61
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.81
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.79
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.49
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.92
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.94
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.69
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.40
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9780.69
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.93
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.42
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.45
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.40
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.86
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11526.25
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.74
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000007000
 
 Normal statistic for number of bits   :   0.055
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.34
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999846515
 
 Normal statistic for number of bits   :   -1.21
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 242                :    0.9985
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:33.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           3.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35173
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.25
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.78
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.40
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.31
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.35
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.90
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.70
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.73
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 58                 :    0.9914
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  8.9e-3
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.64
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.48
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.30
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.14
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908305
   j =  2                              :            45843
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908393
   j =  2                              :            45796
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    5.31
 p-value of test no 92                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.90
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.35
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.91
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.31
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.17
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.79
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 127                :  4.3e-4    *****
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 128                :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   73.39
 p-value of test no 129                :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.55
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.10
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17662.68
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.66
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.99
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.20
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.41
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.05
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.62
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.20
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.47
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.47
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.00
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.89
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.43
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.07
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.66
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.21
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.82
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.95
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.63
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.12
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.70
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.80
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.68
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.71
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.61
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.73
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.21
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.71
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.56
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.60
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.02
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.76
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.44
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.36
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.21
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.51
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.97
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.55
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.68
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.49
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.89
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999921026
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.32
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000029272
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:34.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35174
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7576
 p-value of test no 15                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.88
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.85
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.36
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.36
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.10
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.66
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.22
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.83
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.64
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.66
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.94
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.12
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.90
 p-value of test no 66                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.48
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.13
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45651
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869651
   j =  1                              :        399908700
   j =  2                              :            45647
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908163
   j =  2                              :            45914
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.18
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.74
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.05
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.98
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.10
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.20
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
 p-value of test no 142                :    0.9972
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17751.40
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.79
 p-value of test no 146                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.31
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.54
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.13
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.58
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.42
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.14
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.46
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.50
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.62
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.42
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.61
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.01
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.45
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.11
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.46
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.81
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.60
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.52
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.46
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.65
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.51
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.04
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.15
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.28
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.37
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.99
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.37
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.83
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.58
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.18
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.50
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.10
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.22
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.72
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.88
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.01
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3952.92
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.04
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.39
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.98
 p-value of test no 231                :  6.8e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999814403
 
 Normal statistic for number of bits   :   -1.47
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.03
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000019492
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:55.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35175
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5544
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     976
 p-value of test no 25                 :  6.4e-3
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.39
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.60
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.42
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.14
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.80
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.41
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.89
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.31
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.37
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.02
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.20
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.75
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.49
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907982
   j =  2                              :            46000
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908322
   j =  2                              :            45833
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.20
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.07
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.32
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.37
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.95
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.52
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.18
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.14
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17514.61
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.71
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.00
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.28
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.68
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.51
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.73
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.95
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.93
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.97
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.19
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.43
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.31
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.20
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.43
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.56
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.71
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.16
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.81
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.31
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.63
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.93
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.15
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.16
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.81
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.90
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.21
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.30
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.47
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.33
 p-value of test no 177                :    0.9900
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.10
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 188                :    0.88
 
 Sample variance                       :    2.03
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.88e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.22
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.90
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 205                :  2.7e-3
 
 Anderson-Darling statistic = A2       :    5.54
 p-value of test no 206                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  259.91
 p-value of test no 207                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.84
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.57
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.02
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.92
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.84
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.60
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.20
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.99
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.90
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999978632
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.01
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000188242
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:41.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35176
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.67
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.07
 p-value of test no 35                 :  8.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.31
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.52
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.37
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.89
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.92
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.10
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.42
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.61
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.01
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.95
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.43
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5139.16
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907799
   j =  2                              :            46096
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908485
   j =  2                              :            45750
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-6
 p-value of test no 110                :    0.9963
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.57
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.50
 p-value of test no 121                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.14
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.96
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.18
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.09
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.18
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.28
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.26
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17480.22
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.72
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.62
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.35
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.85
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.75
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.71
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.01
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.43
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.03
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.56
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.10
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.07
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.94
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.79
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.74
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.12
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.20
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.86
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.29
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.80
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  440.26
 p-value of test no 169                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.54
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.32
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.00
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.37
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.51
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.35
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.34
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.39
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.84
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.99
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.88
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9729.99
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.19
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.80
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.83
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.50
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.77
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11665.48
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.64
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000073126
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.05
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999943283
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35177
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 10                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.68
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.93
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.06
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.30
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.77
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.85
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.95
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.24
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.83
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.68
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.69
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.69
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.49
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.75
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.20
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46144
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870144
   j =  1                              :        399907716
   j =  2                              :            46136
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908657
   j =  2                              :            45664
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.19
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.84
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.15
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.01
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.48
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.22
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.15
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.89
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.16
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.51
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.62
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.80
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.52
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.87
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.94
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.65
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.92
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.67
 p-value of test no 156                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.04
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.27
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.65
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.81
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.37
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.77
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.16
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.41
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.43
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.63
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5237.42
 p-value of test no 168                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.83
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.70
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.56
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.99
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.65
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.63
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.66
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.50
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.79
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 194                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.58
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.71
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.44
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10293.86
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10327.87
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.10
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.94
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.01
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.79
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.16
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12241.22
 p-value of test no 230                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.30
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000063166
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.87
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000092650
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.36e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:36.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35178
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7088
 p-value of test no 20                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.46
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.23
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.68
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.37
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.16
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.98
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.38
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.92
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.07
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.77
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.18
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.50
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.33
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908203
   j =  2                              :            45897
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908855
   j =  2                              :            45571
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.43
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.40
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.02
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.09
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.26
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.20
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.38
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.06
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.92
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.66
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17538.16
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.95
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.50
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.94
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.18
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.96
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.86
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.27
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.66
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.38
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.14
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.39
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.64
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.05
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.48
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.35
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.75
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.14
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.76
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.05
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.03
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.12
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.19
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.31
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.13
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.35
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.97
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.30
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.15
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.96
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.54
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.01
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.06
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.34
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.40
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.14
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 218                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.51
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.30
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.68
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.69
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.43
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12072.76
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.32
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000185734
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.19
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999978911
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.080
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:20.98
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35179
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4176
 p-value of test no 14                 :    0.9928
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.81
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.62
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.79
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.21
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.95
 p-value of test no 53                 :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.90
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.62
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.79
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7252.80
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.26
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 63                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.58
 p-value of test no 64                 :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  100.28
 p-value of test no 65                 :  8.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.08
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.42
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.64
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908472
   j =  2                              :            45755
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908081
   j =  2                              :            45958
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.71
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   37.46
 p-value of test no 120                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.35
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.09
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.28
 p-value of test no 123                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.17
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.25
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.94
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.47
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.69
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.87
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.30
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.67
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.41
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.11
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.64
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.07
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.17
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.82
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.98
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.48
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.08
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.14
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.03
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.50
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.91
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.86
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.14
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.66
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.27
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.87
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.56
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.58
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.52
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.41
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.68
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.08
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.06
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.60
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.90
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.69
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.49
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.30
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.90
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.63
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.87
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.58
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.65
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.31
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.64
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000018145
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.16
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999932291
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9959
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:20.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35180
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5535
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7494
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     826
 p-value of test no 25                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.12
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.79
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.75
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.77
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.12
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.81
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1527.55
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.54
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.45
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.90
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.44
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.22
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.71
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45425
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869425
   j =  1                              :        399909154
   j =  2                              :            45417
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908127
   j =  2                              :            45935
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.67
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.54
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.26
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.64
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.03
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.76
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 131                :    0.9911
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.80
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.42
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17401.35
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.33
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.61
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.41
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.11
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.04
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.91
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.87
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.43
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.22
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.60
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.27
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.56
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.17
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.63
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.48
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.93
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.54
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.55
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.28
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.87
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.54
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.08
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.45
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.63
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.12
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.23
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.03
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.66
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.74
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.51
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.14
 p-value of test no 198                :  3.2e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 201                :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.94
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 204                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 206                :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  270.70
 p-value of test no 207                :  6.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.21
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.77
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.93
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.86
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.44
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.03
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.24
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.87
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.65
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000027913
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.21
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999971297
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:08.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        6.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35181
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4230
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.17
 p-value of test no 23                 :  7.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.58
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.62
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.04
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  501.58
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.44
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.96
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.85
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.27
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.61
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.27
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4901.78
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908096
   j =  2                              :            45949
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908819
   j =  2                              :            45586
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.94
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.51
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.32
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.44
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.25
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.90
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.74
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.34
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.21
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.31
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.05
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.66
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.07
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.12
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.71
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.99
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.44
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.36
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.18
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.22
 p-value of test no 155                :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.31
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.76
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.32
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.91
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.34
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.00
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.30
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.36
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.06
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.21
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.99
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.42
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5194.03
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.86
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.09
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.26
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.00
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.74
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.21
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.56
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.21
 p-value of test no 176                :    0.9938
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.11
 p-value of test no 178                :  7.4e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.28
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.57
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.49
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10286.55
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.61
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.24
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.59
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.64
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.89
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.84
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.07
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000128866
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.62
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999943799
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.46
 p-value of test no 243                :    0.9930
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35182
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 5                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 9                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.61
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    3.04
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.24
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.45
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.32
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.03
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.98
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.36
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.53
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  285.15
 p-value of test no 54                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.75
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.49
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.18
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.26
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.91
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.10
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.82
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5186.60
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908766
   j =  2                              :            45605
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46307
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870307
   j =  1                              :        399907389
   j =  2                              :            46301
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.80
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.70
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.92
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.19
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.05
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.85
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 142                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17085.47
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.70
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.53
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.27
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.84
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.13
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.45
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.83
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.72
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.50
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.03
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.09
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.56
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.91
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.49
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.33
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.09
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.66
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.72
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.54
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.84
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.64
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.80
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.78
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.56
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.76
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.53
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.60
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.12
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.37
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.78
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.69
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.56
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.25
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.03
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.70
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.63
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.47
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.38
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.13
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11859.99
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11461.85
 p-value of test no 230                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.19
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000039853
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.81
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999875225
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:46.64
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35183
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 11                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     964
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.14
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.28
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.09
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.42
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.86
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.58
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.02
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.35
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.62
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.15
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.66
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.70
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.78
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.62
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.25
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.14
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908031
   j =  2                              :            45977
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908122
   j =  2                              :            45930
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.36
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.32
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.27
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.68
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.97
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.74
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.45
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.95
 p-value of test no 135                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.90
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17756.75
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.09
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.87
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.28
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.55
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.65
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.94
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.96
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.14
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.24
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.00
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.11
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.21
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.20
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.89
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.27
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.09
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.57
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.90
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.86
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.31
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.95
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.49
 p-value of test no 170                :    0.9938
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.93
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.85
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4822.44
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.99
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.86
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.48
 p-value of test no 176                :  4.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.06
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.64
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.46
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.96
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9651.80
 p-value of test no 215                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.14
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.81
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.90
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.54
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.26
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.27
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.27
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999854003
 
 Normal statistic for number of bits   :   -1.15
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.12
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000009073
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-3
 p-value of test no 245                :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.78
 p-value of test no 248                :  2.7e-3
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:15.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35184
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9925
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.07
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.15
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.80
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.09
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.25
 p-value of test no 53                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.38
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.85
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.26
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.98
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.07
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.46
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.56
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.10
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.11
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907805
   j =  2                              :            46090
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908009
   j =  2                              :            45988
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 90                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-4
 p-value of test no 101                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.14
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.29
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.05
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.19
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.33
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.88
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.62
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.83
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17768.57
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.84
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.68
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.50
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.15
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.06
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.57
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.33
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.27
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.73
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.00
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.43
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.67
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.15
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.19
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.05
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.13
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.24
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.29
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.61
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.75
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.42
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.03
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.85
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.91
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.81
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.19
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.33
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.38
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.16
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.86
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.24
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.08
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.65
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.53
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10205.22
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.045
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 220                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5073.70
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.74
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.50
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.36
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.48
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.46
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.99
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000006148
 
 Normal statistic for number of bits   :   0.049
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.86
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999886085
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
 p-value of test no 236                :    0.9965
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 238                :    0.9946
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.96
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:04.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35185
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 29                 :    0.9962
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.91
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.99
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.25
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.86
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.86
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.85
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.19
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.82
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.08
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.58
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908001
   j =  2                              :            45998
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45558
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869558
   j =  1                              :        399908890
   j =  2                              :            45546
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 93                 :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.76
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.70
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.39
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.47
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.19
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.47
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.35
 p-value of test no 125                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.80
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.89
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 142                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17790.76
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.42
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.84
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.86
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.36
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.65
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.50
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.99
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.95
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.81
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.61
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.26
 p-value of test no 158                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.72
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.11
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.91
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.86
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.52
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.61
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.89
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.83
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.08
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.94
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.12
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.88
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.39
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.77
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.34
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.57
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.58
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.76
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 188                :  7.6e-3
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.38
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.69
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.76
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.67
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 213                :    0.9904
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9689.65
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.90
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.94
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.79
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.37
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.57
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.86
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.53
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000005230
 
 Normal statistic for number of bits   :   0.041
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.21
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999967934
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:40.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35186
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5377
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 22                 :    0.9982
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.95
 p-value of test no 35                 :  9.7e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    4.01
 p-value of test no 36                 :  8.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     251
 p-value of test no 37                 :    0.9980
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.23
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.53
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.62
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.10
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.86
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.80
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.97
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.23
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.19
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.72
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.74
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.88
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.29
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.92
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907761
   j =  2                              :            46115
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908611
   j =  2                              :            45693
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 86                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  8.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
 p-value of test no 106                :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.09
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.82
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.56
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.74
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.30
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.05
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.45
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.50
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.18
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17365.07
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.18
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.45
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.00
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.43
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.55
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.61
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.18
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.89
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.24
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.88
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.17
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.46
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.34
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.30
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.17
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.59
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.56
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.18
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.47
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4859.90
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.27
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.48
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.57
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.66
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4739.53
 p-value of test no 173                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.22
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.87
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.09
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.44
 p-value of test no 177                :    0.9926
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.10
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.55
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.91
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.98
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.74
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.94
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.36
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.28
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.97
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.95
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.70
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.92
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.89
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000152059
 
 Normal statistic for number of bits   :    1.20
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.98
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999968189
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 250                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:56.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35187
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 21                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.46
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.66
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.94
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.75
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.08
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.93
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.19
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1318.69
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6798.25
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.25
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.53
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.95
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5063.48
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908443
   j =  2                              :            45777
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908343
   j =  2                              :            45824
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  4.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.37
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.62
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.07
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.51
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.31
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.70
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.12
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.55
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.72
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.33
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.83
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.52
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.09
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.16
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.20
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.61
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.57
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.37
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.46
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.94
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.08
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.77
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.78
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.92
 p-value of test no 161                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.57
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.92
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.03
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.64
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.03
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.39
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.92
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.61
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.03
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.71
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.67
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.49
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.79
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.97
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.12
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.75
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.59
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.03
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.16
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.97
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.25
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.14
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.22
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.89
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.78
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.46
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.84
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.96
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000091333
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.00
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999891386
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 250                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.32
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35188
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5299
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.74
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9944
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    3.08
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.93
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.05
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.44
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.02
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.25
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.72
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.12
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.29
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.35
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.02
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.67
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.69
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.56
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4930.70
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907886
   j =  2                              :            46057
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46046
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870046
   j =  1                              :        399907911
   j =  2                              :            46040
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 73                 :  2.7e-3
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 104                :    0.9906
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.24
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.99
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.13
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.65
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.99
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.46
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.72
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.23
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.84
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.07
 p-value of test no 146                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.08
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.80
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.39
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.88
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.40
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.60
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.59
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.99
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.24
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.79
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.03
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.08
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.20
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.77
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.16
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.67
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.14
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.11
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.49
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4763.77
 p-value of test no 168                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.28
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.29
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.02
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  463.05
 p-value of test no 172                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5101.93
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.31
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.79
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.16
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.32
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.43
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.25
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.78
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.19
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 212                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10359.61
 p-value of test no 215                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.63e-4
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.76
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.15
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.04
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.98
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.88
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.02
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.46
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999953153
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.80
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000072976
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.33
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:24.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35189
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.49
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.06
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.47
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.25
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.61
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.57
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.73
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.63
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.84
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.23
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.81
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.07
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.91
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908492
   j =  2                              :            45751
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908674
   j =  2                              :            45657
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.32
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.77
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.08
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.09
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.15
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.24
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.06
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.91
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.79
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.94
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.97
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.90
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.32
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.96
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.70
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.23
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.49
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.73
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.93
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.53
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.41
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.28
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.81
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.37
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.79
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.75
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.07
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.72
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.34
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.81
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.86
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.44
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.08
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.78
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.62
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.92
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.41
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.22
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 185                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 188                :    0.9921
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.34
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.38
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.84
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.70
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.21
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.05
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5041.78
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.15
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.09
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.33
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.78
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.21
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999924155
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.34
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000144901
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35190
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 5                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5584
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.98
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.59
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.92
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.97
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.83
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.19
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.19
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.16
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.33
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.19
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.13
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5150.65
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908167
   j =  2                              :            45912
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908355
   j =  2                              :            45818
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.22
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.99
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.86
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.97
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.16
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.97
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.47
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.38
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.41
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.58
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.31
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.77
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.24
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.22
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.07
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.76
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.44
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.26
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.19
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.25
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.92
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.75
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.32
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.09
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.98
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.11
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.55
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.49
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.89
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.74
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.78
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.44
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.58
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.39
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.97
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.63
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.18
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.32
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.67
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.90
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.40
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.37
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.069
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.50
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
 p-value of test no 200                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.11
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.32
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.77
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.54
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.082
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.92
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.87
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.88
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.09
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12053.49
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.04
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.76
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999985718
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.57
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000098959
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35191
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997197
   j =  2                              :             1400
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.00
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.52
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.60
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.54
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.77
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.98
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.57
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.16
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.07
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.54
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.63
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.34
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908153
   j =  2                              :            45916
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908117
   j =  2                              :            45934
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.82
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.48
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.69
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.54
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.67
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 127                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.43
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.65
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.01
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.29
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.03
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.78
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.67
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.86
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.35
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.96
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.20
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.50
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.49
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.02
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.16
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.69
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.98
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.61
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.50
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.49
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.79
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.65
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.09
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.74
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.22
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.49
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.70
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.53
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.60
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.27
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.91
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.34
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.29
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.90
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.10
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.99
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.76
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.38
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.28
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.51
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4678.29
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.11
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.09
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.24
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11742.41
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.23
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000088246
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.77
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000090349
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35192
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    4.86
 p-value of test no 27                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.05
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.70
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.91
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.17
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.14
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.06
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  499.86
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.28
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.50
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.30
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.14
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.81
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.82
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.94
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907952
   j =  2                              :            46018
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908445
   j =  2                              :            45773
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.06
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.22
 p-value of test no 120                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.06
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.97
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.00
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.98
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.92
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.15
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.46
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.20
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.94
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.81
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.86
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.02
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.96
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.06
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.19
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.59
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.91
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.19
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.80
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.66
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.68
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.71
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.30
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.02
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.20
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.19
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.46
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.42
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.04
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.99
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.87
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5287.13
 p-value of test no 173                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.72
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.19
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.17
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.30
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.12
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.64
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.33
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10185.58
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.42
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.16
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.09
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.44
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.65
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.29
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.66
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000156880
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.61
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000066931
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 238                :    0.47
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 253                :    0.47
 
 Sample variance                       :    2.18
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35193
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.97
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9951
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 44                 :    0.9934
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.63
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.45
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.79
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.09
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.38
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.86
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.86
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.84
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.07
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.40
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.27
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.51
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908059
   j =  2                              :            45960
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908177
   j =  2                              :            45907
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.33
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.62
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.91
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.15
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.51
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.86
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.76
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.28
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.57
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.86
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.65
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.10
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.92
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.03
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.55
 p-value of test no 153                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.33
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.18
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.26
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.34
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.91
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.36
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.94
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.52
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.04
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.00
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.62
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.24
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.06
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.05
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  285.90
 p-value of test no 169                :    0.9999    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.44
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.47
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.74
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.36
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.32
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.27
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.41
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.87
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.01
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.54
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.83
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.55
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.67
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4361.29
 p-value of test no 227                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.12
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.80
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.62
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.43
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999883316
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.79
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000015604
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)    0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35194
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.49
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.40
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.43
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.75
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.23
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.86
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.17
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.63
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.52
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.31
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.05
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.88
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.58
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.80
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908584
   j =  2                              :            45705
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908276
   j =  2                              :            45859
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 90                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.66
 p-value of test no 117                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.05
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.96
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.09
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.21
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.33
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.07
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.18
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.92
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.36
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.83
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.60
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.27
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.28
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.27
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.26
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.09
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.00
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.35
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.69
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.57
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.23
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.75
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.65
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.43
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.14
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.63
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.57
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.14
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.25
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.94
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.74
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.45
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.19
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.28
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.08
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5215.83
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.35
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.81
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.18
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    2.18
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.80
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.34
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.03
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.87
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.12
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10260.21
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.69
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.91
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.65
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.32
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.46
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11630.75
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.27
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999985676
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.13
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000099643
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.78
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35195
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7147
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.79
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.64
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.91
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.37
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.81
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.65
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.28
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.58
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.83
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.04
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.76
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.07
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5113.95
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908007
   j =  2                              :            45995
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907590
   j =  2                              :            46196
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.38
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.81
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.87
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.87
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.90
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.00
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.82
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.49
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.68
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.70
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.19
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.97
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.71
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.49
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.46
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.41
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.97
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.81
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.50
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.00
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.58
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.78
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.70
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.04
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.88
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.85
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.22
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.99
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.48
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.43
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.52
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.38
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.83
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.83
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.39
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.51
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.34
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.25
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.59
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.09
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.55
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.21
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11560.80
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.37
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000058441
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.73
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000086212
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35196
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9958
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.11
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.20
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.67
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.51
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.40
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.14
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.85
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.61
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.43
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7111.23
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.28
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.54
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.63
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.37
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907979
   j =  2                              :            46003
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45793
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869793
   j =  1                              :        399908419
   j =  2                              :            45783
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 101                :    0.9941
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.69
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.08
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.73
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.11
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.92
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.80
 p-value of test no 125                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.06
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.96
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17854.47
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.61
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.31
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.76
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.00
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.82
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.36
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.75
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.27
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.92
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.35
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.94
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.63
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.07
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.61
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.24
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.71
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.24
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.43
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.59
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.15
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.19
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4832.58
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.54
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.85
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.07
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.07
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.36
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.85
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.83
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.87
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.020
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.84
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4685.65
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.26
 p-value of test no 227                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.76
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.69
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.61
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.28
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999886802
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.65
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999990905
 
 Normal statistic for number of bits   :  -0.072
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    2.00
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:40.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35197
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7150
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    2.92
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.83
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.97
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.18
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.91
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  386.26
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.66
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.23
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.57
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 62                 :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    6.42
 p-value of test no 64                 :  6.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   35.74
 p-value of test no 65                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.32
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.29
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46352
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870352
   j =  1                              :        399907299
   j =  2                              :            46346
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.039
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.10
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.59
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.58
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.36
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.57
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.94
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.12
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.53
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.72
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17103.62
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.88
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.59
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.32
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.30
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.28
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.64
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.88
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.23
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.42
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.84
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.00
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.62
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.72
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.27
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.32
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.45
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.55
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.62
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.21
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.23
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.76
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.70
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.86
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.34
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.47
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.47
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.46
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.43
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.21
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.84
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.33
 p-value of test no 178                :    0.9928
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.48
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.20
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.37
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.59
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.08
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.12
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.39
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.18
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.32
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.16
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.26
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.48
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000016177
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.97
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000004681
 
 Normal statistic for number of bits   :   0.037
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:35.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35198
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 4                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.63
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.18
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.68
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.46
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.80
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  289.47
 p-value of test no 54                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.09
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.36
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.48
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.79
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.39
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.32
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.13
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4860.81
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46221
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907559
   j =  2                              :            46219
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908591
   j =  2                              :            45700
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 118                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.45
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.00
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.56
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.07
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.57
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.35
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.63
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17336.53
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.23
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.60
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.54
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.18
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.12
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.42
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.72
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.23
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.24
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.48
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.82
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.54
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.20
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.29
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.07
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.27
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.82
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.58
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.37
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.70
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.72
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.79
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.79
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.48
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.14
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.93
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.33
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.46
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.40
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.70
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 186                :  4.2e-3
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 188                :    0.05
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.61
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.99
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.68
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.47
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.04
 p-value of test no 218                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.69
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5007.88
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.03
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.66
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.68
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.06
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.65
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000078001
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.70
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000113485
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:24.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35199
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.78
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.76
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.70
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.65
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.85
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.85
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.95
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.34
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.06
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.51
 p-value of test no 65                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.99
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.97
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.60
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907925
   j =  2                              :            46030
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908194
   j =  2                              :            45897
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.52e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.09
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.40
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.64
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.13
 p-value of test no 122                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.76
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.14
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.50
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.02
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.92
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.13
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17611.85
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.61
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.27
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.02
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.56
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.53
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.37
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.59
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.01
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.10
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.65
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.14
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.28
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.73
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.81
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  188.13
 p-value of test no 164                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.82
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.09
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.68
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.70
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.83
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.94
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.44
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.37
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.68
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.41
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.04
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.17
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.23
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.53
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.89
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.64
 p-value of test no 203                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 204                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.04
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9998.50
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.28
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.76
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.27
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.76
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.83
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.94
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.59
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.23
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000061021
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.15
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999887432
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.69
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:26.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35200
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 6                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4523
 p-value of test no 16                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.95
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.86
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.46
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.70
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.32
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.17
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.37
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.04
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.77
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  509.64
 p-value of test no 55                 :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.08
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.73
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.71
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.60
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.26
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.24
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.86
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908223
   j =  2                              :            45884
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907522
   j =  2                              :            46236
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
 p-value of test no 104                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.04
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.20
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.99
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.09
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.86
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.63
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.79
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.99
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.32
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17208.24
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.16
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.46
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.34
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.88
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.60
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.72
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.75
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.40
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.24
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.97
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.79
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.63
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.43
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.26
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.16
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.57
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.52
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.46
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.34
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.24
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.07
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.84
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.64
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.29
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.15
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.42
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.60
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.88
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.04
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.79
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.44
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.29
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9784.94
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.40
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.52
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.43
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.70
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.08
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.89
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.89
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000183271
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.66
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999941849
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    2.91
 p-value of test no 239                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:37.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35201
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 9                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.68
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.42
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.56
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.90
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.56
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.92
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.21
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.12
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7154.62
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.88
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.93
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.30
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.47
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.51
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908182
   j =  2                              :            45903
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45621
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869621
   j =  1                              :        399908761
   j =  2                              :            45615
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.00
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.59
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.91
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.11
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.33
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.64
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.83
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.42
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.52
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.70
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.62
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.92
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.30
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.79
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.02
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.46
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.46
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.52
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.21
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.10
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.48
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.53
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.81
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.75
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.73
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.90
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.91
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.38
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.08
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.00
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.81
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.86
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.70
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.96
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.98
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.24
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.66
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.85
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.30
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    3.64
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9656.38
 p-value of test no 215                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
 p-value of test no 220                :    0.9964
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.76
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.77
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.96
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.26
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12141.81
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.25
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.55
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000106297
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000109939
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.080
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:34.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35202
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 10                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.91
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.74
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.83
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.73
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.09
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.86
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.56
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.14
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.70
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.42
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.00
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.78
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.20
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.95
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.95
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.03
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908571
   j =  2                              :            45713
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45541
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869541
   j =  1                              :        399908920
   j =  2                              :            45537
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.91
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.89
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.79
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.61
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.39
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.05
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.35
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.13
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.30
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.82
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.49
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.04
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.87
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.19
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.20
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.94
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.58
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.69
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.02
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.85
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.89
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.96
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.17
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.59
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.80
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.81
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.00
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.32
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.60
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.37
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.50
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.00
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.89
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.57
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.45
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.94
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.74
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.56
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.58
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.29
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.07
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.13
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.79
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.59
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11662.87
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.92
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.57
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000064039
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.86
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999974783
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.78e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:35.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35203
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.36
 p-value of test no 34                 :  2.1e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.57
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.62
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    3.71
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.66
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.24
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.89
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.53
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.07
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.64
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.46
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.23
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.07
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.88
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.27
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.94
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.05
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908454
   j =  2                              :            45764
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907929
   j =  2                              :            46031
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.86
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.93
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.17
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.09
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.75
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.31
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.50
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.22
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17603.78
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.78
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.48
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.04
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.14
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.96
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.16
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.95
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.13
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.91
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.07
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.47
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.56
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.55
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.70
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.75
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.87
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.63
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.93
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.91
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.70
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.22
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.87
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.41
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.06
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.48
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.88
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5212.94
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.70
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.85
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.21
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.83
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.53
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.24
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.54
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.88
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.29
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.23
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.97
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.56
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.66
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.39
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.59
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000029458
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.15
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999971450
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-4
 p-value of test no 236                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 238                :    0.9940
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:00.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35204
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.47
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.20
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.15
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.02
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.73
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.05
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1543.21
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.48
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.68
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.99
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.65
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.35
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.09
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908432
   j =  2                              :            45775
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908745
   j =  2                              :            45623
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 87                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    6.47
 p-value of test no 88                 :  6.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.8e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.35
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.11
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.01
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.18
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.90
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.81
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.48
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.11
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.68
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.58
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.23
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.23
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.13
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.73
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.74
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.99
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.00
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.77
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.76
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.96
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.98
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.35
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.81
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.98
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.96
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.11
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.01
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.37
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.30
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.79
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.73
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.73
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.16
 p-value of test no 171                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.71
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.11
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.66
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.36
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.96
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.34
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.80
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.23
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.89
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.97
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.06
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.19
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.95
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.94
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.37
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.39
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.78
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.97
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000039031
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.67
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000119407
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:58.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  48  MaxOft, t = 24                  3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35205
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 12                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     660
 p-value of test no 31                 :  8.3e-3
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.92
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.33
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.43
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.69
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.91
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.64
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.86
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.01
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.37
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.19
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.58
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.79
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.38
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.82
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.56
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.28
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.72
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907727
   j =  2                              :            46129
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908255
   j =  2                              :            45865
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
 p-value of test no 87                 :    0.9901
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.68e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.72
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.46
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.83
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.71
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.51
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.87
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.48
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.84
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.06
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.96
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.26
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.54
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.42
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.78
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.57
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.39
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.98
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.05
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.74
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.11
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.29
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.64
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.26
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.29
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.44
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.55
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.23
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.06
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.93
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.65
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.46
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.30
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.36
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.69
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.47
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.17
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.26
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.30
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.15
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.20
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.33
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.40
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.89
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.42
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.28
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.03
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4319.78
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.73
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11421.95
 p-value of test no 229                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.66
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.17
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000101767
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.01
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999991568
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:44.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35206
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 9                  :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.97
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.39
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.01
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.72
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.63
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.25
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.00
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.55
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.42
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.21
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.17
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908090
   j =  2                              :            45949
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908728
   j =  2                              :            45633
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 94                 :    0.9913
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.05
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.19
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.16
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.70
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.62
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.63
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.68
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 128                :    0.9931
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.44
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.07
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.72
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.47
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.47
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.03
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.50
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.39
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.07
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.37
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.86
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.82
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.84
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.53
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.13
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.50
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.34
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   96.98
 p-value of test no 164                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.80
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.56
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.91
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.75
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.70
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.20
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.06
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.98
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.42
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.39
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.40
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.39
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.63
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.04
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.08
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.46
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.97
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9761.41
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.41
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.04
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.54
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.33
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.60
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.91
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.66
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999909182
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.32
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000045763
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
 p-value of test no 251                :    0.9970
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 253                :    0.99
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35207
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.45
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.39
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.53
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.28
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.27
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.17
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.68
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.41
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.01
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.62
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.48
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.45
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.90
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.61
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.40
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908175
   j =  2                              :            45911
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908517
   j =  2                              :            45731
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 115                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.64
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.94
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.57
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.28
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.70
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.42
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.41
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.92
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.11
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17228.90
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.08
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.41
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.61
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.14
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.05
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.28
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.52
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.12
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.33
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.06
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.68
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.26
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.98
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.32
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.33
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.77
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.58
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.96
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.77
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.60
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4783.02
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.42
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.28
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.03
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.48
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4684.76
 p-value of test no 173                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.90
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.41
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.28
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.69
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.02
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.30
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.85
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.24
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.67
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.38
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.56
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.12
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.51
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000097498
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999991475
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:37.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35208
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.81
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.32
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.24
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.52
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.62
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.08
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.56
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.18
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.61
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.26
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.02
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.34
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46334
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870334
   j =  1                              :        399907337
   j =  2                              :            46324
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908297
   j =  2                              :            45847
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.64
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.13
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.03
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.44
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.99
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.90
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.82
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.80
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.92
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17843.86
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.67
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.01
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.56
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.72
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.77
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.29
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.02
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.62
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.42
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.37
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.23
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.21
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.61
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.52
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.24
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.60
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  435.04
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.46
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.66
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.71
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.59
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.83
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.41
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.69
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.29
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.28
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.55
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.17
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.52
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.80
 p-value of test no 176                :  5.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.55
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.52
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.21
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.75
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.54
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.75
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.21
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.25
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4311.78
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.04
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.49
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.79
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.00
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000094576
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.59
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000149749
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35209
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1501
 p-value of test no 10                 :  1.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334621
   j =  1                              :        599996998
   j =  2                              :             1501
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    2.39
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.42
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.98
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.89
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.82
 p-value of test no 49                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.96
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.57
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.71
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.78
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.62
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.55
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.55
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.17
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.53
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.05
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.42
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.16
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907528
   j =  2                              :            46227
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908160
   j =  2                              :            45920
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9911
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.56
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  112.75
 p-value of test no 120                :  4.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.08
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.66
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.28
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.84
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.98
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.10
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.30
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.18
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.23
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17092.65
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.01
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.41
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.53
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.72
 p-value of test no 149                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.63
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.21
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.51
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.51
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.60
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.21
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.23
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.23
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.66
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.49
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.03
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.20
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.19
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.75
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.62
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.52
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.35
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.45
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.49
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.66
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.29
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.54
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.02
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.89
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 192                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.94
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.20
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.45
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.78
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.80
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.70
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.74
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.04
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.31
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.81
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.00
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999975467
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.88
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999913781
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.63
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:44:21.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           1.4e-4
  60  WeightDistrib, r = 20           4.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35210
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.29
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.99
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.86
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.27
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.14
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  517.58
 p-value of test no 55                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.76
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7035.91
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.59
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.21
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.24
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.36
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.23
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908757
   j =  2                              :            45611
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46241
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870241
   j =  1                              :        399907519
   j =  2                              :            46239
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
 p-value of test no 86                 :    0.9944
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.34
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.10
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.60
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.99
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.88
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.31
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.50
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.97
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.74
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17266.24
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.19
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.95
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.24
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.09
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.97
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.00
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.73
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.32
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.29
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.66
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.97
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.62
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.87
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.02
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.16
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.34
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.34
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.37
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.57
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.46
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.72
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.29
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.66
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.32
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.37
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.48
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.40
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.90
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.03
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.89
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 218                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.76
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.66
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.78
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.56
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.29
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.72
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.36
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000070936
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.96
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000033730
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 238                :    0.52
 
 Sample variance                       :    2.90
 p-value of test no 239                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.77
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:59.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35211
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5474
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.61
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.83
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.08
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.34
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.02
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.07
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.95
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.27
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.18
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.80
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.01
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.34
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.95
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4936.55
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908480
   j =  2                              :            45757
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45627
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869627
   j =  1                              :        399908750
   j =  2                              :            45619
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.49
 p-value of test no 120                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.66
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.77
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.60
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.46
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.79
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.19
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.27
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17201.26
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.89
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.82
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.28
 p-value of test no 149                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.40
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.78
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.67
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.69
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.77
 p-value of test no 156                :    0.9959
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.48
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.90
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.35
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.64
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.68
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.28
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.72
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.53
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.89
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.19
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.09
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.27
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.49
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.93
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.16
 p-value of test no 171                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.11
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.40
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.71
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.81
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.36
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.35
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.07
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.58
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.31
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.99
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.07
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.04
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.49
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.75
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.88
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.54
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.09
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999893429
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.22
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000039457
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:15.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35212
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5595
 p-value of test no 13                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7098
 p-value of test no 15                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.06
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.81
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.36
 p-value of test no 50                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.39
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.24
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.67
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.43
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.91
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7227.74
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.06
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.61
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.23
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.93
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907882
   j =  2                              :            46056
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908644
   j =  2                              :            45672
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
 p-value of test no 76                 :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 103                :  3.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    4.99
 p-value of test no 105                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.65
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.59
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.02
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.63
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.16
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.71
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.56
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.25
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.88
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.39
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.66
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.38
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.04
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.83
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.36
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.43
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.55
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.76
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.46
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.02
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.21
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.50
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.73
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.36
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.63
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.54
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.34
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.24
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.34
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.07
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.76
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.83
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.08
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.52
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.59
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.25
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.45
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.06
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.93
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.45
 p-value of test no 178                :    0.9914
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.59
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.90
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.57
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.23
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.60
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.70
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.85
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.64
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.96
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.20
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.82
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.75
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.74
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000029983
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.97
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999937721
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:13.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35213
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    3.69
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.13
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.96
 p-value of test no 41                 :  9.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.38
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.45
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.93
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.46
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.82
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.72
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7383.36
 p-value of test no 57                 :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.27
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.36
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.89
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.61
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.09
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45697
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869697
   j =  1                              :        399908608
   j =  2                              :            45693
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45514
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869514
   j =  1                              :        399908973
   j =  2                              :            45512
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.54
 p-value of test no 119                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.11
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.37
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.82
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.57
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.36
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.52
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.77
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17436.28
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.94
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.32
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.01
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.67
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.89
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.41
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.43
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.67
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.72
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.71
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.53
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.14
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.19
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.98
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.54
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.17
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.85
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.24
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.11
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.23
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.69
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.48
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.38
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.02
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.12
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.27
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.76
 p-value of test no 178                :  3.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.12
 p-value of test no 179                :    0.9991    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.53
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.28
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.46
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.89
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -4.04e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.69
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.65
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.23
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.34
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.54
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.13
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.58
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000166768
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.85
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000013291
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    2.02
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 29              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35214
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.95
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.88
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.36
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.88
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.56
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.95
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.80
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.30
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.24
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.97
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.75
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.96
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5241.27
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908170
   j =  2                              :            45912
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908283
   j =  2                              :            45854
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 83                 :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.70
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.95
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.72
 p-value of test no 121                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.72
 p-value of test no 122                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.72
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.87
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.46
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.66
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.32
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.21
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.29
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17747.35
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.81
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.21
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.77
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.90
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.91
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.00
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.10
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.41
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.06
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.58
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.73
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.27
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.53
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.32
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.40
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.57
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.97
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.60
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.50
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.23
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.38
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.91
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  245.45
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.57
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.86
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.78
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.22
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.71
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.10
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.80
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.48
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.02
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.82
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.48
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.15
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.25
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.42
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.31
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.49
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.99
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.72
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.89
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.17
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000104830
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.85
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999934922
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:57.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35215
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.46
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.30
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.80
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.11
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.74
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.32
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.40
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.69
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.69
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.52
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.24
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.09
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908491
   j =  2                              :            45747
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907907
   j =  2                              :            46042
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.15
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.01
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.39
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.87
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.72
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.04
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.57
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.61
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.14
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.89
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.67
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.23
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.89
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.79
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.73
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.06
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.55
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.52
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.29
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.90
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.97
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.02
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.17
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.70
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.96
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.07
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.73
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5137.47
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.10
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.17
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.19
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.40
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.35
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.49
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.98
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.57
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.15
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.75
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.20
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.95
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.47
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.00
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.58
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.68
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.29
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.76
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.83
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.26
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.54
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000083851
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.43
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999961913
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 235                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 253                :    0.91
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:50.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35216
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.21
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.10
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.68
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   44.42
 p-value of test no 48                 :  5.0e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.59
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.53
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.24
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.10
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.72
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.61
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.12
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.60
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.51
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.26
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.56
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.13
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.59
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908112
   j =  2                              :            45935
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907771
   j =  2                              :            46113
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 94                 :    0.9939
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.04
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.83
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.44
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.71
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.90
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.43
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.96
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.69
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.15
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.88
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.54
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.65
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.83
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.60
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.33
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.22
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.45
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.04
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.34
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.92
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.85
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.71
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.90
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.93
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.66
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.24
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.00
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.07
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.62
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.72
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.97
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.87
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.40
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.79
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.87
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.71
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.13
 p-value of test no 184                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.26
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 201                :    0.9933
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.80
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.31
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.14
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.68
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-3
 p-value of test no 219                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  3.0e-3
 
 Anderson-Darling statistic = A2       :    4.13
 p-value of test no 221                :  7.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5182.48
 p-value of test no 222                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.0e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5076.08
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.59
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.20
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12111.98
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.19
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.42
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999903119
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999955514
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:08.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35217
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7499
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4165
 p-value of test no 16                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    4.62
 p-value of test no 24                 :  4.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :    1005
 p-value of test no 25                 :  3.1e-4    *****
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.29
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.68
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.01
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.59
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.72
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.97
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.16
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.84
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.45
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.05
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 63                 :  2.3e-4    *****
 
 Anderson-Darling statistic = A2       :    6.17
 p-value of test no 64                 :  8.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   94.89
 p-value of test no 65                 :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.62
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.82
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.75
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45743
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869743
   j =  1                              :        399908516
   j =  2                              :            45739
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908587
   j =  2                              :            45705
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.21
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.92
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.77
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.23
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.28
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.29
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.26
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.31
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.63
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.29
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.49
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.68
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.40
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.87
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.19
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.30
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.48
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.96
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.79
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.37
 p-value of test no 156                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.60
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.45
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.52
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.56
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.87
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.84
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.32
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.41
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.34
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.75
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.42
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.31
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.34
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.39
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.79
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.63
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.32
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.74
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.42
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.40
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.26
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.22
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.01
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.80
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.98
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.31
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.13
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.24
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.00
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.59
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.02
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999996029
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.36
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000047281
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 247                :  4.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.91
 p-value of test no 248                :  1.8e-3
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:11.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NJumps, t = 3        3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35218
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.29
 p-value of test no 23                 :  2.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.20
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.69
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.11
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.63
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.44
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.40
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1563.25
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7012.43
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.31
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.23
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.86
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.87
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4897.77
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908256
   j =  2                              :            45866
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46248
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870248
   j =  1                              :        399907513
   j =  2                              :            46230
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.34
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.42
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.89
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.05
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.32
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.56
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.49
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.45
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.08
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.37
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.28
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.83
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.16
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.91
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.66
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.05
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.87
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.94
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.03
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.97
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.85
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.75
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.69
 p-value of test no 161                :    0.9926
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.29
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.03
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.98
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.68
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.53
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.23
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.36
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.49
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.00
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  489.97
 p-value of test no 172                :  2.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5150.61
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.60
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.09
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.064
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 190                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.32
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 202                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  257.69
 p-value of test no 203                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.69
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.18
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.17
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5093.23
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.15
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.15
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.50
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.08
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.27
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.58
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000054274
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.02
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999943763
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:06.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 M (L=10000, r=15)   2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35219
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    3.93
 p-value of test no 30                 :  9.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.82
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.77
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.29
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.52
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.67
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.71
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.28
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.19
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.51
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.07
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.63
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.94
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.80
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908131
   j =  2                              :            45933
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908253
   j =  2                              :            45872
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-4
 p-value of test no 109                :  2.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-5
 p-value of test no 110                :    0.9958
 
 Anderson-Darling statistic = A2       :    7.83
 p-value of test no 111                :  1.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.55
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.85
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.54
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.31
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.28
 p-value of test no 123                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.40
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.19
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.56
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.43
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.69
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.81
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.28
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.86
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.96
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.99
 p-value of test no 153                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   51.27
 p-value of test no 154                :  9.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.57
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.06
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.96
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.75
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.14
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.19
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.62
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.45
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.47
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.95
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.56
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.07
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.09
 p-value of test no 167                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.56
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.90
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.65
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.33
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.60
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.20
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.42
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  258.14
 p-value of test no 175                :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.70
 p-value of test no 176                :  6.1e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.25
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.32
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.03
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.64
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.50
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.90
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.36
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.32
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.34
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.42
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.13
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.43
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.96
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.43
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000008776
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.38
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000022912
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:25.78
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0               1.4e-4
  75  RandomWalk1 R (L=50, r=25)      9.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35220
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 32                 :    0.9986
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.66
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.67
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.93
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.38
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.35
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.38
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.80
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.61
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.41
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.72
 p-value of test no 59                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    5.69
 p-value of test no 60                 :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   55.63
 p-value of test no 61                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 64                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.35
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.14
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.35
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.10
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908304
   j =  2                              :            45845
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46270
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870270
   j =  1                              :        399907463
   j =  2                              :            46264
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.06
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.01
 p-value of test no 122                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.11
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.47
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.66
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.27
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.38
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.31
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17652.74
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.28
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.20
 p-value of test no 147                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.86
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.49
 p-value of test no 149                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.75
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.60
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.49
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.56
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.74
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.41
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.55
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.78
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.47
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.80
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.30
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.81
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.85
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.33
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.85
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.10
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.07
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.10
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.41
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.38
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.76
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.32
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.24
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.87
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.62
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.54
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.48
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.63
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10155.19
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9959.24
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.028
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.28
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.20
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.42
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.29
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12007.72
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.21
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.94
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999915581
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.71
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000057862
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:10.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35221
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7036
 p-value of test no 18                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    3.16
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     638
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    3.65
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.14
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.10
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.01
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.17
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.41
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.53
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.84
 p-value of test no 52                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.90
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.74
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.85
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.21
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.78
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.69
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.89
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.30
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.80
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.90
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908263
   j =  2                              :            45864
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907988
   j =  2                              :            46003
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 87                 :  2.6e-3
 
 Anderson-Darling statistic = A2       :    6.07
 p-value of test no 88                 :  9.4e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  7.6e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 115                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.88
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.64
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.90
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.65
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.02
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.71
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.94
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.64
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17267.65
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.67
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.39
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.08
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.21
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.03
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.27
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.38
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.37
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.91
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.93
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.47
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.94
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.19
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.34
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.45
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.08
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.91
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.92
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.59
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.60
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.10
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.46
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.32
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.79
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.50
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.85
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.20
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.66
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.62
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.097
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.99
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   43.00
 p-value of test no 199                :  5.7e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.76
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.34
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.37
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
 p-value of test no 212                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.39
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 219                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.86
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.83
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.74
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.67
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.07
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.61
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.20
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000034633
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.77
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000020668
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         0.9995 
  48  MaxOft, t = 24                  7.6e-4
  87  LongestHeadRun, r = 27          5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35222
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     838
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.44
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9972
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.50
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.70
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.45
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.55
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.70
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.68
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.89
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.25
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.25
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.54
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.85
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.58
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.74
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908443
   j =  2                              :            45774
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
 p-value of test no 86                 :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.09
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.76
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.58
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.66
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.61
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 138                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.30
 p-value of test no 141                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.56
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.98
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.66
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.29
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.51
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.72
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.20
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.83
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.50
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.30
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.19
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.88
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.07
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.60
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.75
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.49
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.83
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.62
 p-value of test no 163                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.88
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.35
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.21
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.22
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.13
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.09
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.75
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.97
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.56
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.91
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.10
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.40
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.80
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.88
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.27
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.34
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.90
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 209                :  4.1e-3
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10343.58
 p-value of test no 211                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.39
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.63
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.53
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.80
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.41
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.99
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.47
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.83
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000007996
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.80
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999898841
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:37.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35223
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9921
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.89
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.66
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.45
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.49
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.34
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.47
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.94
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.40
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.74
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.37
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-4
 p-value of test no 63                 :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.44
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.28
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.21
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.63
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908679
   j =  2                              :            45653
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46112
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870112
   j =  1                              :        399907781
   j =  2                              :            46102
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.52
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.84
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.00
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.26
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.15
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.34
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.82
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17381.35
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.80
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.26
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.89
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.55
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.41
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.68
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.03
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.43
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.21
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.81
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.69
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.13
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.16
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.46
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.86
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.36
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.41
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.60
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.94
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.29
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.45
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.40
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.00
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.65
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.32
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.74
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.84
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.59
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.01
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.90
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.61
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.30
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.25
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.44
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.92
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.29
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.01
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.40
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3892.38
 p-value of test no 228                :    0.9940
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.08
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.28
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.22
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999981716
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.02
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999856823
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:11.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35224
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7109
 p-value of test no 15                 :    0.9929
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     846
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.42
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.03
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.49
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.25
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.17
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.89
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.87
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.25
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.70
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.21
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.61
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.47
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.73
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908563
   j =  2                              :            45714
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907754
   j =  2                              :            46120
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.48e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.05
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.13
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.30
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.13
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.03
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.77
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.61
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.93
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17611.32
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.96
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.34
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.61
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.91
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.56
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.81
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.27
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.67
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.92
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.16
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.39
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.14
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.57
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.92
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.56
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   42.69
 p-value of test no 165                :    0.9987
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.35
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.83
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.25
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.70
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.11
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.24
 p-value of test no 171                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.80
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.50
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.83
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.21
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.33
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.51
 p-value of test no 179                :    0.9940
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.76
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.75
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.42
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.49
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.64
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.26
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.79
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.36
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.88
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.20
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.74
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000090406
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.10
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999891707
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:36.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35225
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.85
 p-value of test no 34                 :  3.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.47
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.99
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.29
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.88
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.28
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.86
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.22
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.96
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.46
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.36
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.41
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.55
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908670
   j =  2                              :            45662
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45601
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908799
   j =  2                              :            45599
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.56
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.79
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.91
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.54
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.20
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.00
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.83
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.15
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.86
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.75
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17555.95
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.09
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.00
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.77
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.89
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.73
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.78
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.43
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   98.33
 p-value of test no 156                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.36
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.66
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.62
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.18
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.64
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.67
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.67
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.51
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.49
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.52
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.12
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.89
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.87
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.05
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.49
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.54
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.29
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.97
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.20
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.26
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.45
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.94
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.63
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.29
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.66
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.07
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.15
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.23
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.86
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.85
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11600.54
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.79
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.50
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999949730
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.97
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000070363
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)     0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35226
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 3                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.85
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.67
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.17
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.77
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.59
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.02
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.52
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.00
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7099.52
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.25
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.74
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.29
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.44
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.61
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45880
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869880
   j =  1                              :        399908243
   j =  2                              :            45874
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45942
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869942
   j =  1                              :        399908119
   j =  2                              :            45936
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  5.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
 p-value of test no 113                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.63
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.75
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.80
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.09
 p-value of test no 124                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.39
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.07
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 131                :    0.9930
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.51
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.23
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 140                :    0.9965
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.03
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.05
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.64
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.71
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.27
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.23
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.40
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   65.01
 p-value of test no 151                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.19
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.74
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.32
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.98
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.73
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.58
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.68
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.81
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.99
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.32
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.33
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.03
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.11
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.18
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.78
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.03
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.28
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.13
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.62
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.88
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.15
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.02
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.42
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.96
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.29
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.88
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.74
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.71
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.76
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.41
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.74
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.33
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.00
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.01
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.13
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.86
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000069844
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.41
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999966113
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35227
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 12                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7560
 p-value of test no 15                 :  2.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4561
 p-value of test no 17                 :  3.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.72
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.47
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.09
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.59
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.65
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.09
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.69
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.52
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.21
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.21
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.93
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.46
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.37
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.41
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908726
   j =  2                              :            45634
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908045
   j =  2                              :            45973
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 76                 :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-4
 p-value of test no 113                :  7.0e-4    *****
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 114                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.30
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.88
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.45
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.04
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.32
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.95
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.04
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.66
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   19.81
 p-value of test no 134                :  1.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.08
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17313.61
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.04
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.09
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.71
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.56
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.30
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.05
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.06
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.73
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.89
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.45
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.30
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.29
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.02
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.84
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.49
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.55
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.51
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.68
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.80
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.29
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.44
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.76
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.29
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.42
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.91
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.87
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.51
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.98
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.68
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.65
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.50
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.85
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.01
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3929.13
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.92
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12052.48
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.11
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.99
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999895229
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.58
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000021937
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         3.7e-4
  68  MatrixRank, L=1000, r=0         1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35228
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.23
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.59
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.32
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.83
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.11
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.81
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.16
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.04
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.31
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   50.07
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.20
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.43
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.07
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.85
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907839
   j =  2                              :            46067
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.71
 p-value of test no 120                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.11
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.00
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.02
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.13
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.16
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   91.27
 p-value of test no 141                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17747.10
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.30
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.30
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.97
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.87
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.01
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.25
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.85
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.10
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.97
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.63
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.26
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.63
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.89
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.94
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.55
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.04
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.24
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.27
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.38
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.26
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.15
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.74
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.38
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.47
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.12
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4727.71
 p-value of test no 173                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.04
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.83
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.01
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.55
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.22
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.75
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.01
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.93
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.25
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.58
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.71
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.51
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.30
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.07
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.60
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.11
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.97
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999975131
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.32
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999838415
 
 Normal statistic for number of bits   :   -1.28
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.026
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35229
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7133
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 36                 :    0.9927
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.54
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.38
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.29
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.15
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.47
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.26
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  285.73
 p-value of test no 54                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.17
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.57
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.95
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.55
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 64                 :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.67
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.68
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.96
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4808.04
 p-value of test no 68                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46251
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870251
   j =  1                              :        399907503
   j =  2                              :            46241
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907669
   j =  2                              :            46158
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 76                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 98                 :    0.9905
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 103                :  1.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.080
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.74
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.47
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.17
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.70
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.53
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.94
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.24
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.36
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.15
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.48
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.75
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.94
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.22
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.74
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.50
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.43
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.69
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.89
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.63
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.48
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.04
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.20
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.00
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.76
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.45
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.63
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.35
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.24
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.88
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  279.59
 p-value of test no 169                : 1 -  4.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.51
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.61
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.94
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.90
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.56
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.07
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.85
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.35
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.81
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.84
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.35
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.11
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.84
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.60
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.89
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12071.22
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.58
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.22
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999999899
 
 Normal statistic for number of bits   : -7.98e-4
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.54
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999977972
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    2.05
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 248                :    0.37
 
 Sample variance                       :    2.03
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)   1 -  4.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35230
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4513
 p-value of test no 14                 :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.58
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 40                 :    0.9937
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    3.02
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.67
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.17
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.85
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.52
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.07
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.00
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1270.27
 p-value of test no 56                 :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6909.68
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.74
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.40
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.77
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45404
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869404
   j =  1                              :        399909197
   j =  2                              :            45394
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908324
   j =  2                              :            45829
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-3
 p-value of test no 87                 :    0.9987
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9928
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.01
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.81
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.19
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.41
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.03
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.36
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.71
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.76
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.79
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.42
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17605.47
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.77
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.24
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.36
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.05
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.07
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.54
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.50
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.04
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  586.87
 p-value of test no 158                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.80
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.79
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.40
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.52
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.12
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.79
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.41
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.20
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.82
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.17
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.03
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  148.66
 p-value of test no 170                :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.92
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.03
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.63
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.33
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.16
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.10
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.44
 p-value of test no 177                :    0.9926
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.51
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.50
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.16
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.49
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.24
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.06
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.85
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.88
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.69
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.20
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.74
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.33
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999807890
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.55
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999942818
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:29.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  36  Gap, r = 0                      0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35231
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 4                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.75
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.16
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.53
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.51
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.37
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.58
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7078.31
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.81
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.49
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.00
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.03
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.41
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908480
   j =  2                              :            45751
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908157
   j =  2                              :            45917
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.80
 p-value of test no 116                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.63
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.37
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.38
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.60
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.80
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.92
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.65
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.27
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.03
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 139                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    4.10
 p-value of test no 140                :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.90
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17673.93
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.11
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.74
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.99
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.07
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.82
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.17
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.13
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.98
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.62
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.88
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.28
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.84
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.00
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.13
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.37
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.58
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.90
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  471.83
 p-value of test no 171                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.14
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.79
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.32
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.75
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.91
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.05
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.70
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.77
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.69
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.46
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.31
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.11
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.51
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.85
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.58
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.43
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000146977
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.44
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999897014
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.92
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35232
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 32                 :    0.9909
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    3.16
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.55
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.09
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.97
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.79
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.29
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.57
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  375.17
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.80
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.76
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.15
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.68
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.52
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.29
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.51
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907900
   j =  2                              :            46047
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908584
   j =  2                              :            45708
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.44
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.34
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.80
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.79
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.42
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.60
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.08
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.57
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.59
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.18
 p-value of test no 136                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.64
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.79
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.48
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.13
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.87
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.76
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.14
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.48
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.51
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.15
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.74
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.21
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.47
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.77
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.66
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  613.70
 p-value of test no 163                :  3.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.44
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.19
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.86
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.79
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.89
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.80
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.12
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.46
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.37
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4694.62
 p-value of test no 173                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.34
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.60
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.87
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.29
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 200                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.43
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.25
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9938
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.92
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.37
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.04
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.84
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.63
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.15
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.10
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.37
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.49
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999928409
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999917117
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    2.21
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:26.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    3.7e-4
  79  RandomWalk1 J (L=10000, r=15)   0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35233
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.32
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.87
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.20
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.56
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.31
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.41
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.53
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.22
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1528.04
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.56
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.20
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.00
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.48
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.34
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908412
   j =  2                              :            45788
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908090
   j =  2                              :            45949
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 117                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.44
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.12
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.96
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.83
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.55
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.25
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.52
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.65
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.17
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.96
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.64
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.13
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.27
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.82
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.80
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.36
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.55
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.04
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.72
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.72
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.39
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.37
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.94
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.11
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.96
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.57
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.13
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.67
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.10
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.89
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.84
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.82
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.55
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.67
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.84
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.75
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.02
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.85
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.14
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.49
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    0.65
 p-value of test no 196                :    0.9997    *****
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.42
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.76
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.40
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.49
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.60
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.28
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.13
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.84
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.72
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11650.29
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.66
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999997088
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.05
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999993068
 
 Normal statistic for number of bits   :  -0.055
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:17.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  86  LongestHeadRun, r = 0           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35234
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7143
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     835
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.98
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.96
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.02
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.58
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.81
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.78
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.77
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.56
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.18
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.83
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.95
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.92
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.44
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4897.04
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46161
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870161
   j =  1                              :        399907682
   j =  2                              :            46153
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907934
   j =  2                              :            46033
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 108                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-5
 p-value of test no 113                :    0.9942
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.93
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.87
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.24
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.10
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.87
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.43
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.86
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.81
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.80
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.78
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.67
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.58
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.08
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.37
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.73
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.22
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.85
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.73
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.86
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.73
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.01
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.95
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.30
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.39
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.78
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.04
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.74
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.34
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.33
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4794.33
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.05
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.50
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.97
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.97
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.72
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.87
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.64
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.61
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.53
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 181                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.21
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.61
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.18
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.90
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.89
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.31
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.41
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4016.88
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.79
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.91
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.63
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000041680
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.50
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999864860
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:16.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35235
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.67
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.63
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.41
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.50
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.13
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.66
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.05
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.25
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.19
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.57
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.16
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.55
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4890.62
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908331
   j =  2                              :            45833
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907891
   j =  2                              :            46050
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.01
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.58
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.23
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.71
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.36
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.18
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.32
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 131                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 132                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.09
 p-value of test no 133                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.55
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.77
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.04
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.53
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.60
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.70
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.90
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.08
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.83
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.04
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.47
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.89
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.34
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.86
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.45
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.31
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.94
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.58
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.57
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.66
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.84
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.09
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.30
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.24
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.53
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.26
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.81
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.31
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.35
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.29
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.62
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.19
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.11
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.30
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.57
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.80
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.85
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.76
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11789.37
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.31
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.24
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999995051
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.74
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000052015
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    2.31
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 246                :  9.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 247                :  7.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.13
 p-value of test no 249                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:03.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35236
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    3.95
 p-value of test no 27                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    4.87
 p-value of test no 39                 :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.64
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.94
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.53
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.00
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.63
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.22
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.95
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7093.39
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.51
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.98
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.99
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.74
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.37
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907974
   j =  2                              :            46004
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908171
   j =  2                              :            45910
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.48
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.58
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.22
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.22
 p-value of test no 122                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.34
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.47
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.73
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.92
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.65
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17120.70
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.33
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.89
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.14
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.89
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.21
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.82
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.26
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.34
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.02
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.73
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.82
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.61
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.98
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.79
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.18
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.05
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.56
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.51
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.44
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.19
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.31
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.82
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.95
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.03
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.86
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.51
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.32
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.81
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.80
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.34
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.03
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.43
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.82
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.29
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.15
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.23
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.50
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.94
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.66
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.13
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.28
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11541.35
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.50
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000123628
 
 Normal statistic for number of bits   :    0.98
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.72
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000119797
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:12.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35237
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1498
 p-value of test no 6                  :  1.9e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334618
   j =  1                              :        599997004
   j =  2                              :             1498
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.03
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.93
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.09
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.51
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.89
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.15
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.17
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.64
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.83
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.99
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.38
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.76
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.02
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.62
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908029
   j =  2                              :            45978
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908652
   j =  2                              :            45668
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  104.25
 p-value of test no 121                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.84
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.38
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.96
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.61
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.86
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.55
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.37
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.37
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.23
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.46
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.41
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.79
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.49
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.38
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.64
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.62
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.23
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.89
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.19
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.29
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.81
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.14
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.99
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.06
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.45
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.31
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.82
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.15
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.60
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.73
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.42
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.86
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.20
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.60
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.30
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.72
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.83
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.76
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.51
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.45
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.98
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.28
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.12
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.23
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.88
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.04
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.56
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.87
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000089701
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.16
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000072049
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 237                :    0.9996    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:47.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   6  CollisionOver, t = 3            1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35238
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.87
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.96
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.19
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.11
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.08
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.84
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.29
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7123.94
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.35
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.28
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.67
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.10
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45563
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869563
   j =  1                              :        399908877
   j =  2                              :            45557
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908344
   j =  2                              :            45825
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.38
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.52
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.04
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.76
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.96
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.86
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.54
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.67
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.27
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.02
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.60
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.49
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.21
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.44
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.40
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.75
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.25
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.54
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.79
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.07
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.40
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.32
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.71
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.52
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.62
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.33
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.56
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.79
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.66
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.62
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.09
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.73
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.74
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.53
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.66
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.46
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.21
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.08
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 185                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 187                :  5.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.56
 p-value of test no 188                :    0.9948
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.53
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.52
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.62
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.06
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.11
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.00
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.09
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.00
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.71
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.52
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.66
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.65
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999811577
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.41
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000120004
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:11.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35239
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 6                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7128
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.49
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.66
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.48
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.23
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.11
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.72
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.26
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.89
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.99
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.81
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.05
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45588
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869588
   j =  1                              :        399908826
   j =  2                              :            45584
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.97
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.83
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.75
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.52
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.81
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.29
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.29
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.42
 p-value of test no 137                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 139                :  5.6e-4    *****
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  165.31
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 143                :    0.9905
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17059.55
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.88
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.77
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.71
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.79
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.69
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.44
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.29
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.16
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.83
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.50
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.82
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   97.56
 p-value of test no 161                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.69
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.02
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.19
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.94
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.44
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.06
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.55
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.25
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.65
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.91
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.36
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.63
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  151.26
 p-value of test no 175                :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.29
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
 p-value of test no 185                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.86
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.62
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.06
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.55
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.96
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.76
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.26
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.04
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.96
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.39
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.22
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.24
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.56
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000047167
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.32
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000006436
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.39
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:33.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35240
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.43
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.12
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.83
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.51
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.77
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.81
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.86
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.45
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.10
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.12
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.86
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.42
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.40
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.78
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908180
   j =  2                              :            45907
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908468
   j =  2                              :            45757
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.36
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.64
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.25
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.43
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.30
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.74
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.82
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.12
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.79
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.75
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.28
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.60
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.01
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.05
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.91
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.10
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.53
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.65
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.89
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.84
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.34
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.34
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.89
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.64
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.62
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.33
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.67
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.82
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.73
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.63
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.55
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.83
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.65
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.25
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.09
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.53
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.89
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.17
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.89
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.03
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.68
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.09
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.96
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11534.82
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.89
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.11
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000291457
 
 Normal statistic for number of bits   :    2.30
 p-value of test no 232                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.87
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000048196
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:53.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35241
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 5                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 10                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 17                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.84
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     665
 p-value of test no 31                 :  4.7e-3
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.56
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.71
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.77
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.55
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.74
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.86
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.15
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.73
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.00
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.50
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.34
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.30
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.03
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.98
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.44
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908061
   j =  2                              :            45962
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908081
   j =  2                              :            45952
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
 p-value of test no 101                :    0.9957
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.62
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.61
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.05
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.45
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.60
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.16
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.84
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.63
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
 p-value of test no 142                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17804.32
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.97
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.80
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.65
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.89
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.70
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.19
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.42
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.02
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.68
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.73
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.30
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.05
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.04
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.17
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.25
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.54
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.00
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.06
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.13
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.67
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.90
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.24
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.58
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.01
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.11
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.18
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.97
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.53
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.34
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.01
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.58
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.62
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.47
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.85
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.95
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.87
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.49
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000108883
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.35
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000199099
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 234                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:02.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35242
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.59
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.54
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.00
 p-value of test no 50                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.40
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.25
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.52
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  511.81
 p-value of test no 55                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.71
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.07
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.04
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.92
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.40
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.77
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.02
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46246
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870246
   j =  1                              :        399907510
   j =  2                              :            46242
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908405
   j =  2                              :            45793
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.46
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.00
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.15
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.62
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.97
 p-value of test no 124                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.14
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.12
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.13
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.96
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.40
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.96
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.89
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.76
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.27
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.40
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.61
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.77
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.05
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.71
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.31
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.11
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.50
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.72
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.43
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.34
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.51
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.90
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.98
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.20
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.99
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.57
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.26
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.31
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.25
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.30
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.55
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.48
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.64
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.99
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 183                :    0.48
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.48
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.64
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.08
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 209                :    0.9928
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9653.26
 p-value of test no 211                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.29
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.49
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.84
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.95
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.09
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.47
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.45
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.41
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000032314
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.60
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999940274
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:27.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35243
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    3.46
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.81
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.41
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.86
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.19
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.09
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.11
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.81
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.74
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.20
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.99
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.80
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.91
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.79
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4966.07
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908117
   j =  2                              :            45934
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908072
   j =  2                              :            45961
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 9.36e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.90
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.76
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.58
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.42
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.57
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.83
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.82
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.20
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.32
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.66
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.41
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.50
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.66
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.40
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.60
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.78
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.28
 p-value of test no 156                :    0.9931
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.50
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.88
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.51
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.86
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.81
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.59
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.03
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.35
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.46
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.35
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.45
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.45
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.61
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.26
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.05
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.55
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.04
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.38
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.96
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.11
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.61
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.28
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.24
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.57
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.93
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.85
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4211.70
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.77
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.98
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.87
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.59
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999975056
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.37
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000151123
 
 Normal statistic for number of bits   :    1.19
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    5.04
 p-value of test no 252                :  2.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.02
 p-value of test no 253                :  1.3e-3
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:07.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35244
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.64
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.10
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.80
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.31
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.98
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.73
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.07
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.60
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.13
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.24
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.38
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.39
 p-value of test no 66                 :    0.9955
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.32
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.66
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908400
   j =  2                              :            45794
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908472
   j =  2                              :            45761
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
 p-value of test no 109                :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.93
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.39
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.76
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.19
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.61
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.40
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.46
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.55
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.77
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.08
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.92
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.44
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.29
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.05
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.52
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.96
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.09
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.47
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.09
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.82
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.54
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.53
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.26
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.20
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.95
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.66
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.49
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.95
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.09
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.39
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.56
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.00
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.12
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.24
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.57
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.74
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.39
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.66
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 181                :    0.9925
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 183                :    0.99
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.44
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.81
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.43
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.05
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.68
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.43
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.79
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.82
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.43
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.09
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.66
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000038401
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.08
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000022156
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 246                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:38.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35245
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 6                  :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 8                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    2.96
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     340
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.14
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.02
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.22
 p-value of test no 49                 :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.77
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.53
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.28
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.13
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.05
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.05
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.73
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.74
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.51
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.47
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.47
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.66
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907846
   j =  2                              :            46071
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908685
   j =  2                              :            45653
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.075
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.31
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.56
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.42
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.39
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.45
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.22
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.55
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
 p-value of test no 143                :    0.9904
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.22
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.68
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.39
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.23
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.11
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.19
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.50
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.49
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.85
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.50
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.32
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.32
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.26
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.70
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.10
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.97
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.63
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.50
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.26
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.32
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.34
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.94
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.31
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.51
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.77
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.67
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.47
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.00
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.28
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.85
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.32
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.09
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.42
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.50
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.63
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.05
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.12
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.65
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.14
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.96
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.31
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.49
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.50
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000074971
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.69
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999777098
 
 Normal statistic for number of bits   :   -1.76
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.20
 p-value of test no 249                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 250                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.35
 p-value of test no 253                :    0.9905
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:23.52
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   6  CollisionOver, t = 3            4.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35246
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4162
 p-value of test no 16                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    3.46
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.43
 p-value of test no 48                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.82
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.45
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.98
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.32
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.19
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.80
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.36
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.84
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.16
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.75
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.76
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.05
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.45
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908423
   j =  2                              :            45781
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908327
   j =  2                              :            45832
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.95
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.64
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.02
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.61
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.11
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.72
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.42
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.73
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.98
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.71
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17581.19
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.97
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.81
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.13
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.40
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.91
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.31
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.65
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.71
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.90
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.31
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.60
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.11
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.33
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.87
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.37
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.09
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.45
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.28
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.59
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.31
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.86
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.44
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.63
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.27
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.08
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.02
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.63
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.07
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.45
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.39
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.02
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.93
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4662.45
 p-value of test no 222                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.36
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.68
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.11
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.70
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.54
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.99
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000027721
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.12
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000024919
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:19.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35247
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.63
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.27
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.17
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.59
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.65
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.63
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.91
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.25
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.67
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.24
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.63
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.50
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.05
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.60
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.05
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907992
   j =  2                              :            45998
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46082
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870082
   j =  1                              :        399907839
   j =  2                              :            46076
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.33
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.80
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.21
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.25
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.55
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.37
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.66
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.04
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 132                :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.02
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.96
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.21
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17249.77
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.62
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.98
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.92
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.84
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.24
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.55
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.75
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.02
 p-value of test no 155                :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.78
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.21
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.57
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.48
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.43
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.27
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.12
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.41
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.63
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.78
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.77
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.71
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.90
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.29
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.47
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.27
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.09
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.65
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.88
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.51
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.19
 p-value of test no 176                :    0.9941
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.49
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.52
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.70
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.89
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.98
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.95
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.38
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.27
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.09
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.90
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.39
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.08
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000044488
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999965972
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.71
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:26.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35248
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 6                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.9909
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    5.91
 p-value of test no 38                 :  1.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.50
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.55
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.09
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.15
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  516.64
 p-value of test no 55                 :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.63
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.82
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.53
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.49
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.71
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.18
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.66
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908607
   j =  2                              :            45689
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908305
   j =  2                              :            45843
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    4.53
 p-value of test no 88                 :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.33
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.25
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.84
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.17
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.34
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.09
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.84
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.99
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.01
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.81
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.98
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.10
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.89
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.87
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.33
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.05
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.63
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.91
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.93
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.53
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.28
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.33
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.33
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.49
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.43
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.78
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.15
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.07
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.32
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.85
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.26
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.07
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.00
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.76
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.30
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5151.45
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.72
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.77
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.39
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 186                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.70
 p-value of test no 188                :    0.9965
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.78
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.55
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.72
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.42
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.36
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.28
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.01
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.48
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.74
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.75
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.95
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.96
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000008476
 
 Normal statistic for number of bits   :   0.067
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999895736
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:45.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35249
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.16
 p-value of test no 29                 :    0.9976
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.17
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.91
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.81
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.24
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.53
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.04
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.63
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.17
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.52
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.64
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.32
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.99
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.27
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46221
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907561
   j =  2                              :            46215
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.87
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.51
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.68
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.12
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.74
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.82
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.19
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.59
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.44
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.82
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.69
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.27
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.14
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.50
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.63
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.53
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.73
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.32
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.27
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.40
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.32
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.50
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.36
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.72
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.42
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.84
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.97
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.32
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.69
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.70
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.95
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.51
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.01
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.63
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.27
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.07
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.44
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.73
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.95
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.50
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.75
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.89
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.51
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.63
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.32
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.75
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.03
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.79
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4272.84
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.42
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.57
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.75
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.13
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999974507
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.35
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000000628
 
 Normal statistic for number of bits   : 4.96e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    2.35
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:50.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35250
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7096
 p-value of test no 15                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.62
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.33
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.22
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.95
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.71
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.10
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.91
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.99
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.27
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.85
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.72
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.86
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.08
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908422
   j =  2                              :            45780
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45457
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869457
   j =  1                              :        399909088
   j =  2                              :            45453
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-5
 p-value of test no 109                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.05
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.67
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.24
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.39
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.45
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.47
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.62
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.51
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.38
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 143                :    0.9918
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17000.30
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.27
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.93
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.49
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.24
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.15
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.46
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.58
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.96
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.71
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.25
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.57
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.33
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.16
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.27
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.46
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.32
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.72
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.30
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.19
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.23
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.50
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.93
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.15
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.04
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.08
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.03
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.02
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.46
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.04
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.39
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.46
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.77
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.20
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.49
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.00
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.99
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.05
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.82
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.73
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000047215
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.34
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000035026
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  8.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.018
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:59.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35251
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4195
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    4.09
 p-value of test no 27                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.28
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.43
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.72
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.84
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.04
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.33
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.82
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.48
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.45
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.72
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.60
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.09
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.09
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.01
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45911
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869911
   j =  1                              :        399908182
   j =  2                              :            45903
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908100
   j =  2                              :            45947
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.78
 p-value of test no 117                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.36
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.24
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.35
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.34
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.29
 p-value of test no 123                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.50
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.52
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.05
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.42
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.94
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.30
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.30
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.61
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.15
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.35
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.53
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.16
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.80
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.76
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.70
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.04
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.01
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.45
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.32
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.13
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.39
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.97
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.44
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.49
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.24
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.54
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.06
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.53
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.66
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.23
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.75
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.82
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.26
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.05
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.99
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.65
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.61
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.67
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.38
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.62
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.45
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11773.90
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.54
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999891266
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999984566
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:36.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35252
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5564
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.29
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.97
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.68
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.51
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.77
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.19
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.50
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.84
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.43
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.19
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.82
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.17
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.86
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907989
   j =  2                              :            46001
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46406
 p-value of test no 71                 :  7.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870406
   j =  1                              :        399907191
   j =  2                              :            46400
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.42
 p-value of test no 118                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.86
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.82
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.90
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.84
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.62
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.87
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.49
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.80
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.86
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.40
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.93
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.08
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.87
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.92
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.03
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.31
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.43
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.20
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.51
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.02
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.34
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.48
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.20
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.23
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.01
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.50
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.32
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.09
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.58
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.35
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.88
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.83
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.81
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.70
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.40
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.21
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.23
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.93
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.25
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.09
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.11
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.48
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.75
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.70
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.85
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.31
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.76
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.38
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12306.81
 p-value of test no 230                :  9.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.77
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999986840
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999999164
 
 Normal statistic for number of bits   : -6.61e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.27
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:58.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      9.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35253
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 6                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.13
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.54
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.17
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.80
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.23
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.66
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.91
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.97
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.64
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.69
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.07
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.63
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.28
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.96
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.29
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.56
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907852
   j =  2                              :            46068
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908205
   j =  2                              :            45896
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.60
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.55
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.35
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.79
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.86
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.25
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.89
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.71
 p-value of test no 134                :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   22.22
 p-value of test no 136                :  1.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.31
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.86
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.06
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.43
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.39
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.95
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.70
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.07
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.96
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.66
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.18
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.19
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.44
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.53
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.84
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.73
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.70
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.39
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.07
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.78
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.61
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.60
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.63
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.51
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.97
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.66
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.60
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.19
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.44
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.09
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 194                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.28
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.16
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.38
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.81
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.78
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.36
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.94
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.88
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.81
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.81
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.13
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000128953
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.78
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000008479
 
 Normal statistic for number of bits   :   0.067
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    2.77
 p-value of test no 239                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    2.04
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.77
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:53.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              1.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35254
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 9                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 16                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.94
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.99
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.75
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.60
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.02
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.23
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.98
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.26
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.22
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.65
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.64
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.68
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.93
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5210.41
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908012
   j =  2                              :            45991
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9909
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.80
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.56
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.38
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.44
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 138                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.49
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17759.08
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.16
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.93
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.26
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.14
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.90
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.87
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.21
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.60
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.56
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.35
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.52
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.98
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.82
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.70
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.02
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.46
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.44
 p-value of test no 165                :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.77
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.38
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.88
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.00
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.28
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.70
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.59
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.10
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  471.91
 p-value of test no 174                :  7.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.36
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.46
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.42
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 188                :    0.47
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.25
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.94
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.54
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.62
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.51
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.76
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.04
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.86
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.97
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.77
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.81
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.86
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.45
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999945272
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.85
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999951152
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:38.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35255
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.73
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.83
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.91
 p-value of test no 52                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.28
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.98
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.62
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.73
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.16
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.61
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.86
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.93
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.24
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.54
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46361
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870361
   j =  1                              :        399907278
   j =  2                              :            46361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.9915
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.34
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.48
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.37
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.21
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.91
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.24
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.63
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.96
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.80
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.11
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.81
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.56
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.26
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.76
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.67
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.33
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.67
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.84
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.33
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.20
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.01
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.64
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.93
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.40
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.15
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.75
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.34
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.17
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.76
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.32
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.99
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.08
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.92
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.68
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.93
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.81
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.12
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.12
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.25
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.10
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.20
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.04
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.88
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4760.08
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.15
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.84
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.57
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11439.52
 p-value of test no 229                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.10
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.52
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999939029
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.62
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000044962
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.72
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:55.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35256
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4510
 p-value of test no 14                 :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.00
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.58
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     183
 p-value of test no 43                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.64
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.18
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.43
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.33
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.96
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.90
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.66
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.99
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.68
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.86
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.62
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.25
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.28
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.01
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908155
   j =  2                              :            45918
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46192
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870192
   j =  1                              :        399907619
   j =  2                              :            46186
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.71
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.37
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.34
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.57
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.34
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.95
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 128                :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.98
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 130                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 132                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.59
 p-value of test no 133                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.96
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.46
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.97
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17242.85
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.15
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.35
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.67
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.93
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.25
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.11
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.01
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.81
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.97
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.55
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.44
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.86
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.45
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.77
 p-value of test no 162                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.88
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.92
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.86
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.17
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.92
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.14
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.18
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.99
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.50
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.42
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.61
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.30
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.32
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.70
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.86
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.48
 p-value of test no 179                :    0.9935
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.21
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.54
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.34
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.47
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.08
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.30
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.18
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.48
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.76
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11512.64
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.18
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.55
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000102628
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.69
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999940076
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 238                :    0.04
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 247                :  9.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.59
 p-value of test no 248                :  4.7e-3
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:54.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35257
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 12                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.56
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.04
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.77
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.76
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.79
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.66
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.56
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.10
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.94
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.69
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6870.66
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-4
 p-value of test no 59                 :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    5.94
 p-value of test no 60                 :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.21
 p-value of test no 61                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.74
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.42
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.29
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908547
   j =  2                              :            45725
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908124
   j =  2                              :            45935
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.61
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.87
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.94
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.38
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.97
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.49
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.27
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.34
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.48
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.07
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.81
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.86
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.02
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.49
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.50
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.23
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.52
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.07
 p-value of test no 155                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.42
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.76
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.77
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.60
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.14
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.53
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.84
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.43
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.76
 p-value of test no 164                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.34
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.59
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.78
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.30
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.68
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.98
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.65
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.68
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.00
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.93
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.37
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.33
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.46
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.20
 p-value of test no 189                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.23
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.75
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9786.19
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.49
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.03
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.50
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.33
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.55
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.29
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.47
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.40
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999944240
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.31
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000068740
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:20.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35258
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.30
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.28
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.11
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.89
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.63
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.39
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.95
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.55
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.71
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.80
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.95
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.05
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.91
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.48
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.07
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908003
   j =  2                              :            45991
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907946
   j =  2                              :            46021
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-4
 p-value of test no 110                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -3.90e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.066
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.01
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.37
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.61
 p-value of test no 121                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.03
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.20
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.41
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.00
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.64
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.19
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.31
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.87
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.27
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.32
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.21
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.48
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.26
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.99
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.79
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.24
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.98
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.24
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.64
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.40
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.58
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.26
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.38
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.76
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.43
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.12
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.37
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.62
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.91
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.89
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.29
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.12
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.94
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.28
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.00
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.60
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.70
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.46
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.80
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.71
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.61
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.00
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.32
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.32
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.52
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.14
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.02
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.74
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999931226
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.84
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000085237
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:38.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35259
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.85
 p-value of test no 46                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.53
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.96
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.20
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.13
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.36
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.98
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.66
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.18
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6933.63
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.13
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.88
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.21
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.34
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.93
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907896
   j =  2                              :            46049
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 97                 :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 98                 :  7.6e-4    *****
 
 Anderson-Darling statistic = A2       :    5.67
 p-value of test no 99                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.83
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.86
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.66
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.14
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.10
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.13
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.22
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.56
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.35
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.28
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.52
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.08
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.75
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.61
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.62
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.66
 p-value of test no 155                :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.32
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.68
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.27
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.63
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.47
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.43
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.59
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.78
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.68
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.90
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.73
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.63
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.64
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.54
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.30
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.24
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.02
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.32
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.33
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.94
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.59
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.37
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.29
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.89
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.62
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.75
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.64
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.28
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.65
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.86
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.55
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000119311
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.97
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000105037
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
 p-value of test no 246                :    0.9948
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.13
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:32.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35260
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.74
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    5.14
 p-value of test no 30                 :  2.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     537
 p-value of test no 31                 :    0.9952
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.49
 p-value of test no 34                 :  1.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.33
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.05
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.20
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.40
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.58
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.02
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.49
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.21
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.64
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.30
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.87
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.03
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.21
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45601
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908800
   j =  2                              :            45597
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908176
   j =  2                              :            45903
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 107                :    0.9927
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.028
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.55
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.10
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.82
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.04
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.12
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.53
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    6.09
 p-value of test no 128                :  9.6e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   80.77
 p-value of test no 129                :  1.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.69
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.74
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.35
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.86
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.83
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.91
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.91
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.53
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.53
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.11
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.17
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.32
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.74
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.24
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.73
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.80
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.94
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.60
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.75
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.85
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.11
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.70
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.31
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4806.56
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.74
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.69
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.48
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.78
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.23
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.53
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.18
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.19
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.14
 p-value of test no 189                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.84
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.40
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.31
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.21
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10075.46
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.93
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.47
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.63
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3926.93
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.45
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.10
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.21
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999946949
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.95
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000110893
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 240                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
 p-value of test no 241                :    0.9965
 
 Anderson-Darling statistic = A2       :    5.50
 p-value of test no 242                :  1.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.27
 p-value of test no 243                :    0.9995    *****
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:59.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  66  MatrixRank, L=30, r=0           1.4e-4
  104  AutoCor, d=3, r=0               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35261
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    2.69
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 32                 :    0.9961
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.29
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.00
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.15
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.25
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.42
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.72
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.79
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.88
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.93
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1334.46
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7214.91
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.11
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.65
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.50
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.60
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4927.61
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908290
   j =  2                              :            45849
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908164
   j =  2                              :            45912
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.60
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.10
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.74
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.27
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.60
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.75
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.98
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.70
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.19
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.23
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17095.83
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.42
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.53
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.46
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.17
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.55
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.11
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.79
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.85
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.59
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.72
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.28
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.42
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.32
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.41
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.03
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.66
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.96
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.38
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.21
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.80
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.50
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.88
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.75
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.43
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.99
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.26
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.68
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.83
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.57
 p-value of test no 179                :    0.9949
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.84
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.98
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.25
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.38
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10224.31
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9760.94
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.00
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.72
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.22
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.03
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.42
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.60
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.89
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999976058
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.49
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000222586
 
 Normal statistic for number of bits   :    1.76
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 238                :    0.51
 
 Sample variance                       :    2.57
 p-value of test no 239                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
 p-value of test no 245                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:38.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35262
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5666
 p-value of test no 13                 :  4.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.62
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.92
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.83
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.87
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.71
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.45
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.54
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.58
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.13
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.47
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.92
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.88
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.53
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.57
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907823
   j =  2                              :            46081
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907764
   j =  2                              :            46115
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.017
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.87
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.57
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.61
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.47
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.55
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.33
 p-value of test no 125                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.21
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.72
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.71
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.68
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17440.42
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.26
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.99
 p-value of test no 148                :    0.9930
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.14
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.71
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.44
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.94
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.16
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.61
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.93
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.08
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.09
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.44
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.51
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.04
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.13
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.13
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.06
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.35
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.73
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.79
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.10
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.35
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.96
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.35
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.61
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.25
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.45
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.42
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.26
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.55
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.37
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9878.68
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.42
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.58
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-4
 p-value of test no 224                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4616.84
 p-value of test no 226                :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.55
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.32
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.72
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12013.35
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.56
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000034408
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.64
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999952601
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 238                :    0.09
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 252                :    0.9985
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.075
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35263
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.38
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.67
 p-value of test no 49                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.56
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.85
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.83
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.94
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  372.31
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.03
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6962.01
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.84
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.06
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   79.72
 p-value of test no 67                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.88
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908401
   j =  2                              :            45795
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907781
   j =  2                              :            46099
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.25
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.90
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.61
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.92
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.23
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.88
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.95
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.82
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.93
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17434.65
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.70
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.69
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.98
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.63
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.29
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.44
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.30
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.25
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.50
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.24
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.47
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.24
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.56
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.14
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.82
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.66
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.60
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.42
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.43
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.06
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.87
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.26
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.96
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.39
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.79
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.28
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.79
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.68
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.53
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.76
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 183                :    0.53
 
 Sample variance                       :    2.62
 p-value of test no 184                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.48
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.11
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.98
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10254.77
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10060.24
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.14
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.13
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.91
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.41
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.05
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.03
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.67
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999961292
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.86
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000120907
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 240                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.97
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  29  SimpPoker, r = 25               0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35264
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4200
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.93
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.48
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.61
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.34
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.42
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.09
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.36
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.63
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.31
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6890.47
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.70
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.84
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.42
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.50
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.69
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908683
   j =  2                              :            45657
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908478
   j =  2                              :            45755
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.45
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.06
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.05
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.37
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.98
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.79
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.13
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.84
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.55
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.81
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17154.33
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.58
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.68
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.49
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.49
 p-value of test no 150                :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.64
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.00
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  191.90
 p-value of test no 156                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.92
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.78
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.50
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.69
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.94
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.53
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.48
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.42
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.94
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.84
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.96
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.51
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.77
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.38
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.71
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.72
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.81
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.28
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.72
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.95
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.72
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.27
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.12
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.01
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.43
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.68
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.96
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.36
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.85
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.41
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.21
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000023374
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.03
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000043642
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    2.30
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35265
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.32
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.51
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.05
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.80
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.38
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.19
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.30
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.39
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.26
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.58
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.58
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.44
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.39
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.04
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.88
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908297
   j =  2                              :            45844
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908275
   j =  2                              :            45858
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-3
 p-value of test no 77                 :    0.9961
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.35
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.72
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.85
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.59
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.94
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.92
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.89
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.79
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.47
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17463.20
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.75
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.82
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.95
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.33
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.36
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.09
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.80
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.43
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.30
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.65
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.86
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.18
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.64
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.13
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.08
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.47
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.80
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.97
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.59
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.48
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.77
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.96
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.15
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.33
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.70
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.84
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.03
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.57
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.28
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.08
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.63
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.99
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10241.94
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.93
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.16
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.01
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.90
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.84
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.20
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.36
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.95
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999813053
 
 Normal statistic for number of bits   :   -1.48
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000016693
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.084
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.14
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:22.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35266
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.24
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.08
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.90
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.95
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.03
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.12
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.82
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.03
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.20
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.08
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.42
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.10
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.49
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.61
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.35
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908119
   j =  2                              :            45939
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908688
   j =  2                              :            45650
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-5
 p-value of test no 112                :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 117                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.68
 p-value of test no 119                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.12
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.93
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.01
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.73
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.99
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.95
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.19
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.07
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17159.54
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.92
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.96
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.20
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.13
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.94
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.90
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.95
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.44
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.30
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.85
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.66
 p-value of test no 156                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.10
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.36
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.41
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.32
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.83
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.88
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.05
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.25
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.84
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.46
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.93
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5180.49
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.98
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.70
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.68
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.51
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.77
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.48
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.52
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.71
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.80
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.42
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.08
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.38
 p-value of test no 203                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.33
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.64
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.77
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.92
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.95
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.39
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.99
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11989.87
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.90
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.52
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000015073
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.76
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999976475
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.19
 p-value of test no 239                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    2.97
 p-value of test no 244                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.42
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:09.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35267
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5331
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.65
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.00
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.98
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.46
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.39
 p-value of test no 53                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.89
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.09
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.47
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7253.26
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.30
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.01
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.38
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.40
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.68
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45447
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869447
   j =  1                              :        399909115
   j =  2                              :            45429
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908418
   j =  2                              :            45782
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.41
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.39
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.26
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.90
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.38
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.52
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.00
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.99
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.66
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 142                :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17748.39
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.53
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.20
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.04
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.94
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.99
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.94
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.04
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.92
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.22
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.08
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.15
 p-value of test no 159                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.23
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.26
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.56
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.98
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.76
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.21
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.01
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.13
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.72
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.68
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.84
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.64
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.65
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.35
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.81
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.89
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
 p-value of test no 200                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.94
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.41
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.38
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.01
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.21
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.18
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.98
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.54
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.70
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.70
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.31
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999946661
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.26
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000048238
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.72e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:04.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35268
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5555
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.76
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.06
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.94
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.75
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.76
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.84
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.37
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.50
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7271.22
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.74
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.55
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.74
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.06
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.54
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908592
   j =  2                              :            45698
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908227
   j =  2                              :            45882
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.036
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.46
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.05
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.90
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.85
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.57
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.84
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.80
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.42
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17340.63
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.18
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.64
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.79
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.51
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.15
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.46
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.65
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.84
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.89
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.35
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.24
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  109.88
 p-value of test no 160                :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.67
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.58
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.31
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.56
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.96
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.53
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.84
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5068.67
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.85
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.35
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.44
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.11
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.15
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.63
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.77
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.19
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.89
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.75
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.07
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.65
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.53
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.53
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.82
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.37
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.82
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.55
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.01
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.74
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.02
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999875864
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.04
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999933851
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.059
 p-value of test no 248                :    0.48
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35269
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.72
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    2.71
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.31
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.30
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.17
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.19
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.43
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.55
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.80
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.58
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.33
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.26
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.96
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.19
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.23
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45475
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869475
   j =  1                              :        399909051
   j =  2                              :            45473
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46184
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870184
   j =  1                              :        399907639
   j =  2                              :            46170
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.86
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.79
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.16
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.08
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.00
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.01
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.43
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.28
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17731.42
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.75
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.16
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.97
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.54
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.78
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.86
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.19
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.49
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.25
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.51
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.62
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.20
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.68
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.06
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.33
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.68
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.00
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.45
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.95
 p-value of test no 164                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.15
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.86
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.95
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.79
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.64
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.05
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.41
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.53
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.92
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.10
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.27
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 192                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.83
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.23
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.81
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.22
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.12
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.03
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.97
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.75
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.30
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.81
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.56
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.58
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000080080
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.46
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000067228
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 6.42e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  84  Fourier3, r = 0                 0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35270
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 10                 :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5427
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.41
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.54
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.55
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.76
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.65
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.01
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.49
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.00
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.61
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.35
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.87
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.59
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.32
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5257.79
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908295
   j =  2                              :            45851
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907851
   j =  2                              :            46064
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 77                 :    0.9923
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.43
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.93
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.03
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.39
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.72
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.33
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.65
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.33
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.89
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.98
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
 p-value of test no 143                :    0.9974
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 144                :  6.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16902.23
 p-value of test no 145                :    0.9978
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.31
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.79
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.03
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.71
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.18
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.39
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.45
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.04
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.98
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.91
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.14
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.59
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.38
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.88
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.27
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.79
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.49
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.20
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.48
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.18
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.21
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.25
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.93
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.49
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.82
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.77
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.08
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.58
 p-value of test no 174                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.43
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.66
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.22
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.56
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.25
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.23
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.44
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.25
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.34
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.19
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.92
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.86
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.63
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11561.76
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.20
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.87
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000293578
 
 Normal statistic for number of bits   :    2.32
 p-value of test no 232                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.44
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000000421
 
 Normal statistic for number of bits   : 3.33e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35271
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.74
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.49
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.58
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.17
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.37
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.65
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.51
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.54
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.36
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.54
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.51
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.38
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.07
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908596
   j =  2                              :            45699
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908023
   j =  2                              :            45987
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.23
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.59
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.60
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.18
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.59
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.97
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.24
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.98
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.52
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.94
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.64
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.98
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.27
 p-value of test no 148                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.75
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.86
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.42
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.65
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.11
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.55
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.27
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.51
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.77
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.82
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.20
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.21
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.13
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.20
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.01
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.93
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.83
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.80
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.02
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.56
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.18
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.86
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.20
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.22
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.37
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.38
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.36
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.24
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.92
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.67
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4837.61
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.84
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.53
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.64
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.28
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.18
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.41
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999997130
 
 Normal statistic for number of bits   :  -0.023
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.38
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999842264
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:53.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35272
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.55
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.75
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.36
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.66
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.38
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.41
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1557.94
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.34
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.21
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.65
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.87
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.02
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.91
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907844
   j =  2                              :            46075
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908724
   j =  2                              :            45632
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 95                 :  7.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9935
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.23e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.63
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.14
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.63
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.80
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.07
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.40
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.15
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.80
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.21
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.37
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17425.91
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.72
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.72
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.95
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.73
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.47
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.80
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.90
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.24
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.39
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.16
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.36
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.13
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.72
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.46
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.47
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.12
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.70
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.54
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.16
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.23
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.97
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.26
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.15
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.06
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.10
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.87
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.39
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.53
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.55
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.28
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.72
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.17
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.03
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.65
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.78
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.53
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.63
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4694.91
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.61
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.11
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.01
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11587.52
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.11
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000007729
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.45
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999985640
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    2.44
 p-value of test no 239                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:12.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35273
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.41
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.43
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.32
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.54
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.71
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.07
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.12
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.36
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.91
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.02
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.98
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.56
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.06
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.41
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.80
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.70
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.15
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45550
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869550
   j =  1                              :        399908902
   j =  2                              :            45546
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908170
   j =  2                              :            45909
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.32
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.69
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.79
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.87
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.42
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.16
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.27
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.47
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.11
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.43
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.83
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.35
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.89
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.97
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.41
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.33
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.16
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.55
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.37
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.72
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.74
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.63
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.11
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.93
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.01
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.67
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.95
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.27
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.80
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.77
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.80
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.94
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.63
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.64
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.72
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4769.99
 p-value of test no 173                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.01
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.79
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.30
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 185                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 187                :  5.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.81
 p-value of test no 188                :  2.4e-3
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.15
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.40
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.93
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.84
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.55
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.46
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.02
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.53
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.40
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.96
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.71
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.11
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000103780
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.78
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999998939
 
 Normal statistic for number of bits   : -8.39e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.22e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.32
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:21.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35274
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 4                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5318
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     818
 p-value of test no 25                 :    0.9971
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9969
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.21
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.77
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.85
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.03
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.20
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.07
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.67
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6805.08
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.01
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.59
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.80
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.49
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.72
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908238
   j =  2                              :            45872
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908550
   j =  2                              :            45719
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.80
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.24
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.78
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.54
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.98
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.71
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.05
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.03
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.44
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17326.75
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.39
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.15
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.49
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.58
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.84
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.91
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.98
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.08
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.30
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.33
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.15
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.49
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.43
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.51
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.19
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.85
 p-value of test no 164                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.37
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.74
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.37
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.68
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.99
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.36
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.07
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.56
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.92
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.57
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.66
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.45
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.72
 p-value of test no 196                :  3.7e-3
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.91
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.27
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.87
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.11
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.21
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.73
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.56
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.98
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.74
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.24
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12110.78
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.40
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999764165
 
 Normal statistic for number of bits   :   -1.86
 p-value of test no 232                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.82
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000042703
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:04.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35275
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.68
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    4.10
 p-value of test no 32                 :  7.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.53
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.38
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.72
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.72
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.60
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.33
 p-value of test no 53                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.16
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.72
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.81
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.96
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.85
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.66
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.80
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4864.16
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46234
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870234
   j =  1                              :        399907534
   j =  2                              :            46230
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908481
   j =  2                              :            45758
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 97                 :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.67
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.56
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.81
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.37
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.09
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.68
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.46
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.15
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.27
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.10
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.98
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.67
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.92
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.13
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.55
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.29
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.29
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.94
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.52
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.96
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.14
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.17
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.48
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.98
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   90.28
 p-value of test no 164                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.99
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.17
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.46
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.49
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.84
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.86
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.44
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.66
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.70
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.97
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.73
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.65
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 181                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.51
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.84
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.10
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.30
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.38
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.61
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4296.17
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.94
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.90
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.86
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.87
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000054670
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.93
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000079282
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9935
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.94
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35276
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9975
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.97
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.17
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.53
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.70
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.99
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.62
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.28
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.88
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  507.06
 p-value of test no 55                 :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.94
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.04
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.37
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.63
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.53
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.62
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4824.66
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908588
   j =  2                              :            45703
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908138
   j =  2                              :            45931
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 80                 :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.73
 p-value of test no 81                 :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  2.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 84                 :    0.9963
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.66
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.55
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.02
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.31
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.47
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.20
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.27
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.31
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.71
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.63
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.43
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.55
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.06
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.38
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.68
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.44
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.19
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.75
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.02
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.62
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.99
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.29
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.94
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.11
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.69
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  434.63
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.23
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.85
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.42
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.48
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.20
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.73
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.03
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.91
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.90
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.61
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.54
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.17
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.80
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.77
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.19
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.57
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.26
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.51
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9717.04
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.23
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.33
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.21
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.08
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.13
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.41
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12077.85
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.59
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999895715
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.25
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999954812
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:57.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35277
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5518
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.87
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.97
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.61
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.44
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.17
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.91
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.12
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.19
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.33
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.26
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.17
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.15
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.52
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4967.25
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46249
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870249
   j =  1                              :        399907505
   j =  2                              :            46243
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908355
   j =  2                              :            45821
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 102                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.53
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.93
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.58
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.19
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.56
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.58
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.80
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.09
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.52
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.85
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.32
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.07
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.12
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.93
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.21
 p-value of test no 155                :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.68
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.06
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.02
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.40
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.85
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.48
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.71
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.87
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.37
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.52
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.19
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.42
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.49
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.35
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.15
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.29
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.77
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.72
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.82
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.62
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.16
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9872.53
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.54
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5101.33
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.59
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.89
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.76
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.29
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11490.21
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.43
 p-value of test no 231                :    0.9974
 
 
 -----------------------------------------------
 Total number of bits:  7999898826
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.86
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999897983
 
 Normal statistic for number of bits   :   -0.81
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:18.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35278
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 10                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5575
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.95
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.86
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.26
 p-value of test no 50                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.51
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.83
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.99
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.90
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7288.71
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.84
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.05
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.46
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.21
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45579
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869579
   j =  1                              :        399908844
   j =  2                              :            45575
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908752
   j =  2                              :            45621
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.01
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.75
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.06
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.39
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.39
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.39
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.62
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 126                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.22
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.82
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.64
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.83
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.16
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.47
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.15
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.43
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.42
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.97
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.85
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.77
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.42
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.42
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.25
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.77
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.54
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.03
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.84
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.67
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.58
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.11
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.49
 p-value of test no 166                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.34
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.97
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.98
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.04
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.41
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.17
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.07
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.63
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.10
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.38
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.43
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.53
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.06
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.13
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.92
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.70
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.52
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.62
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.55
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.91
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.25
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.51
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999826997
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.31
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999919985
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:00.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35279
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 11                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4521
 p-value of test no 16                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.52
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.84
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.59
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.48
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.56
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.73
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1358.21
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7085.47
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.16
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.50
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.71
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.01
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.90
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907915
   j =  2                              :            46035
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45431
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869431
   j =  1                              :        399909140
   j =  2                              :            45427
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 79                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.80
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.78
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.62
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.36
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.58
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.99
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.90
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.72
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.87
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17020.33
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.47
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.73
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.28
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.51
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.17
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.12
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.62
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.91
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.19
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.92
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.69
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.12
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.19
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.27
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.59
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.07
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.61
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.72
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.33
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.21
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.23
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.38
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.88
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.12
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.90
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.68
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.75
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.70
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.41
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.56
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.11
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.54
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.54
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.08
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.72
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.67
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.63
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.39
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.13
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11568.99
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.18
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000199828
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.88
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000179800
 
 Normal statistic for number of bits   :    1.42
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 248                :    0.51
 
 Sample variance                       :    2.08
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:56.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35280
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 9                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.80
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    3.18
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.91
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.48
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.42
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.04
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.70
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.86
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.28
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.22
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.12
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.60
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.15
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.61
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4901.93
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908048
   j =  2                              :            45973
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45362
 p-value of test no 71                 :    0.9922
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869362
   j =  1                              :        399909280
   j =  2                              :            45354
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.87
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.93
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.94
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.85
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.58
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.54
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.08
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.89
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.42
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17419.87
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.57
 p-value of test no 146                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.55
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.90
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.24
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.53
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.97
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.06
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.58
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.46
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.71
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.16
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.75
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.11
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.82
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.21
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.04
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.67
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.16
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.16
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.69
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.21
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.16
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.39
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.77
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.82
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.89
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.89
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.76
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.67
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 183                :    0.18
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.98
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.86
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10239.62
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.20
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.43
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.39
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.36
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.94
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.25
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12091.95
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.47
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999979487
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.37
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000155320
 
 Normal statistic for number of bits   :    1.23
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:07.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35281
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1488
 p-value of test no 12                 :  5.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334608
   j =  1                              :        599997024
   j =  2                              :             1488
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.95
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.96
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.35
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.21
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.25
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.65
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.53
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.28
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6843.50
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.96
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.94
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.14
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.72
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907915
   j =  2                              :            46038
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908592
   j =  2                              :            45701
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
 p-value of test no 97                 :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 106                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 108                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.83
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.70
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.09
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.64
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.99
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.45
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.88
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.56
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.04
 p-value of test no 134                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.19
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17046.19
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.21
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.30
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.60
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.51
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.68
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.42
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.37
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.65
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.63
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.71
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.42
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.12
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.11
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.14
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.44
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.80
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.31
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.25
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.28
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.56
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.98
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.64
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.75
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.86
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.65
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.71
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.90
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.60
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.17
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 188                :    0.11
 
 Sample variance                       :    2.21
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.25
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.86
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.62
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.81
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9898.20
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.66
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.97
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.58
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.79
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3964.84
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.70
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.31
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.02
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000013783
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000038170
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:18.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           5.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35282
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4189
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9909
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.96
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.37
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.51
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.15
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.04
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.20
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.68
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.14
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7241.58
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.17
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.72
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.65
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.91
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.67
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908802
   j =  2                              :            45596
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45486
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869486
   j =  1                              :        399909034
   j =  2                              :            45474
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.23
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.97
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.18
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.20
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.24
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.75
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.29
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.11
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.80
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.26
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.02
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.08
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.12
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.24
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.91
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.80
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.59
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.03
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.21
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.93
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.25
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.63
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.14
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.79
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.52
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.01
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.80
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.63
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.35
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.61
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.20
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.07
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.54
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.93
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.12
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.57
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.65
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.56
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.82
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.21
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.07
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.22
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.15
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.31
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.38
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.34
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.09
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.15
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.29
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.39
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.95
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999963818
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.54
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000087436
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.72
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:28.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35283
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.75
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.58
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.27
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.13
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.75
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.37
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.78
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.20
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.76
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.45
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.91
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.94
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.19
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.11
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907812
   j =  2                              :            46085
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907962
   j =  2                              :            46016
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.92
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.17
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.63
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.29
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.31
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   52.28
 p-value of test no 125                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.43
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.84
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.76
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.42
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.30
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.94
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.50
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   58.20
 p-value of test no 148                :  1.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.49
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.17
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.42
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.91
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.56
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.77
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.37
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.47
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.80
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.95
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.91
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.38
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.20
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.72
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.14
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.54
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.64
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.55
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.82
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.46
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.48
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.49
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.61
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.14
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.20
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.47
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.27
 p-value of test no 203                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.97
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.44
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9807.50
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
 p-value of test no 220                :    0.9971
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.49
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.73
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.76
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.93
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.58
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.91
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.96
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000121150
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.46
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000038338
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:05.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       1.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35284
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5370
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    3.46
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.67
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.34
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.21
 p-value of test no 48                 :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.41
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.89
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.33
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.95
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.75
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.32
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.33
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.35
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.53
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.95
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.79
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5259.87
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908757
   j =  2                              :            45614
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908600
   j =  2                              :            45700
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.74
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.20
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.19
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.67
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.29
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.00
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.78
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.57
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.88
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.33
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.97
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.02
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.85
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.46
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.43
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.11
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.98
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.84
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.29
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.82
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.82
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.40
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.80
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.54
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.05
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.27
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.99
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.42
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.84
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.91
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.00
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.87
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.11
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.93
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.07
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.25
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.54
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.83
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.85
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.89
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.61
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.51
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4745.69
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.59
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.23
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.86
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.65
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.20
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.59
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000115825
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.13
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999914804
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:08.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35285
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.55
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    3.02
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     342
 p-value of test no 37                 :  9.3e-3
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.95
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.39
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.60
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.72
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.32
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.56
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.04
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.56
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.27
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.45
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.70
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.78
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.02
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908069
   j =  2                              :            45961
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45658
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869658
   j =  1                              :        399908686
   j =  2                              :            45654
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 100                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.07
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.50
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.25
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.96
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.68
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.76
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.99
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.97
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.81
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.64
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.13
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.16
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.29
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.73
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.67
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.65
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.29
 p-value of test no 156                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.41
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.71
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.49
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.14
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.47
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.76
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.80
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.39
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.15
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.58
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.26
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.41
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.71
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.60
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.51
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.60
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.36
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.46
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.16
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.64
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.70
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.75
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.07
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.43
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.82
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5063.07
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.12
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.50
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11563.74
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.09
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999870764
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.19
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999984866
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:57.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35286
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5365
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.07
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.02
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.07
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.50
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   89.32
 p-value of test no 52                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.42
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.61
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.28
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.47
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.70
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.49
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.24
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.82
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5199.45
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908480
   j =  2                              :            45757
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45682
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869682
   j =  1                              :        399908638
   j =  2                              :            45678
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.91
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.17
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.67
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.36
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.76
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.12
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.72
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.80
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.52
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.45
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.33
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.44
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.80
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.63
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.85
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.51
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.05
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.77
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.51
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.36
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.18
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.42
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.57
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.98
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.78
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.97
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.29
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.36
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.17
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.56
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.13
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.63
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.68
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.93
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.57
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.65
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.03
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.24
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.96
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.78
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.04
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.93
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.29
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.74
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4685.09
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.09
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.65
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.98
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.86
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.91
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999967979
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.75
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000070504
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35287
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5534
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7093
 p-value of test no 19                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     968
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    3.68
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 42                 :    0.9984
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.62
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.03
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.72
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.22
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.69
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.65
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.38
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.60
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.51
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.32
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.88
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.34
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.52
 p-value of test no 66                 :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.55
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.85
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45586
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869586
   j =  1                              :        399908838
   j =  2                              :            45566
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908218
   j =  2                              :            45885
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.97
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.81
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.42
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.76
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.48
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.21
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.40
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.71
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.10
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.73
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.51
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.04
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.59
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.72
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.04
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.96
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.99
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.32
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.03
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.72
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.22
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.68
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.79
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.28
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.17
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.92
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.92
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.99
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.46
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.47
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.28
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.48
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.54
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.61
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.48
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.59
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.43
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    2.27
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.17
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.37
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.53
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.35
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.65
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.84
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.05
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.73
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.10
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.60
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11448.52
 p-value of test no 229                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.98
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.65
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999921494
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.89
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999952601
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 235                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 236                :  1.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.20
 p-value of test no 237                :  8.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.44
 p-value of test no 238                :  2.9e-4    *****
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               2.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35288
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.97
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.24
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.63
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.87
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.81
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.21
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.28
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.15
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.31
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.19
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.38
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.33
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.37
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.08
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.10
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.79
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.29
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907884
   j =  2                              :            46052
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907727
   j =  2                              :            46135
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.25
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.64
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.50
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.06
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.26
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.48
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.33
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.78
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.12
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.30
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.67
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.71
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.25
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.32
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.55
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.78
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.04
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.01
 p-value of test no 155                :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.31
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.04
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.66
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.04
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.76
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.24
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.90
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.50
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.63
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.13
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.39
 p-value of test no 167                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5246.24
 p-value of test no 168                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.63
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.90
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.95
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.08
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.50
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.51
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.33
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.25
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.00
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.77
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.87
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10180.90
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.09
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5073.91
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.82
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.42
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.22
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.53
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.76
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000031126
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.84
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000110899
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:16.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35289
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5595
 p-value of test no 13                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 34                 :    0.9981
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.77
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.79
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.57
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.86
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.89
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.92
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.64
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7309.45
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.61
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.14
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.52
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.71
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45605
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869605
   j =  1                              :        399908792
   j =  2                              :            45601
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908605
   j =  2                              :            45690
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.76
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.72
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.67
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.34
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.92
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.08
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.76
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.48
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.71
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 140                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.36
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17557.38
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.42
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.53
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.84
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.78
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.71
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.64
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.98
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.76
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.44
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.36
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.92
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.67
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.97
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.61
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.14
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.32
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.08
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.93
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.27
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.41
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.71
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.43
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.16
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.15
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.82
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.30
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.47
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.58
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.03
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.13
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.43
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.46
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10253.69
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 213                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10294.08
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.23
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.43
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.21
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.64
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.19
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.46
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.78
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999893531
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.62
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000008329
 
 Normal statistic for number of bits   :   0.066
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:11.64
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35290
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.61
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.95
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.87
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.53
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.66
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.30
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.00
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.42
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1548.27
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6952.09
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.63
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.44
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.30
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.46
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908080
   j =  2                              :            45954
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908567
   j =  2                              :            45712
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.61
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.28
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.12
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.05
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.44
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.93
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.75
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.63
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.88
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.37
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.79
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.85
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.32
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.13
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.42
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.41
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.58
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.72
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.09
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.94
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.37
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.31
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.31
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.92
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.95
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.84
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.36
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.13
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.29
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.48
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.54
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.39
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.86
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.99
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.08
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.78
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.24
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.65
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 204                :    0.9924
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.10
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.10
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-4
 p-value of test no 213                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9674.37
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.24
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.54
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.52
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.59
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.70
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.02
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.79
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999973649
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.70
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999941648
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.65
 
 Sample variance                       :   0.065
 p-value of test no 249                : 1 -  5.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35291
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5203
 p-value of test no 13                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.31
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.50
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.21
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.84
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.63
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.30
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.86
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.88
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.41
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.98
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.46
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.66
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.37
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5053.45
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908483
   j =  2                              :            45757
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45324
 p-value of test no 71                 :    0.9953
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869324
   j =  1                              :        399909357
   j =  2                              :            45314
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 87                 :    0.9957
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.19
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.64
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.54
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.11
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.23
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.24
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.32
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.55
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.52
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.14
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.55
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.26
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.88
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.68
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.91
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.07
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.53
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.42
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.67
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.88
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.80
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.74
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.66
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.69
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.69
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.71
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.60
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.26
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.87
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.29
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.09
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.01
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.89
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.27
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.96
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.38
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.95
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.62
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.27
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.50
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.94
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.04
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.55
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.79
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.19
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.86
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4329.11
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4029.30
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.14
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.08
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.11
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000083638
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.99
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000089719
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:02.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35292
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5214
 p-value of test no 13                 :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    3.20
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.89
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.78
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.00
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.05
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.03
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.73
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.02
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  200.45
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.12
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1552.24
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.35
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.42
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.88
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.71
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.51
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908807
   j =  2                              :            45589
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907946
   j =  2                              :            46024
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.41
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.58
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.42
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.06
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.64
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.35
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.99
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.20
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.00
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.78
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.94
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.56
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.53
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.07
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.79
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.24
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.47
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.41
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.78
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.86
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.91
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.29
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.54
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.69
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.69
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.50
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.82
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.95
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.51
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.23
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.14
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.90
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.07
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.39
 p-value of test no 175                :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.23
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.88
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.10
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.85
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.29
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.92
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.81
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.30
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.61
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.11
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.41
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.71
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.08
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.69
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999980831
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.07
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000012169
 
 Normal statistic for number of bits   :   0.096
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.16
 p-value of test no 254                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:48.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35293
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 42                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.30
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.35
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.99
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.68
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.13
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.87
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.37
 p-value of test no 53                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.63
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.91
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.48
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.85
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.06
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.66
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.53
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.83
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4856.14
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46230
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870230
   j =  1                              :        399907543
   j =  2                              :            46224
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45425
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869425
   j =  1                              :        399909154
   j =  2                              :            45417
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.66
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.91
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.34
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.23
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.87
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.36
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.89
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.47
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.07
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.27
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.45
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.26
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.79
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.89
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.97
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.62
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   41.84
 p-value of test no 155                :  7.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.49
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.59
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.11
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.50
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.89
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.76
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.99
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.50
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.21
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.21
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.86
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.58
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.64
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.81
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.04
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.52
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.78
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.56
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.50
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.32
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.65
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.35
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.14
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.79
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.76
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.06
 p-value of test no 216                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.95
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.91
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.50
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.80
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.19
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.05
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.69
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999869873
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.38
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000131032
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:29.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 C (L=50, r=25)      7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35294
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7540
 p-value of test no 15                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.20
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.85
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.04
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.10
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.64
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.66
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.62
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.13
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.90
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.51
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.30
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.02
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.98
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908362
   j =  2                              :            45813
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.19
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.77
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.17
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.00
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.11
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.36
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.43
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.53
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 130                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 131                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 132                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.13
 p-value of test no 133                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.90
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17481.05
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.10
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.69
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.84
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.28
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.32
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.19
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.61
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.10
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.04
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.56
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.04
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.58
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.16
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.45
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.37
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.27
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.41
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.01
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.42
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.91
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.78
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.62
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.72
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.53
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.98
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.37
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.08
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.93
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.40
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.26
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.01
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.82
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.51
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.50
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.96
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.61
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.53
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.09
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11310.50
 p-value of test no 230                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.62
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000114832
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.87
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999909182
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.88
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35295
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    3.13
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.66
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.02
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.32
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.93
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.62
 p-value of test no 51                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.01
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.83
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.37
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.79
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.86
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.91
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.06
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.06
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.30
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.92
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.24
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908196
   j =  2                              :            45899
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908393
   j =  2                              :            45799
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    4.21
 p-value of test no 102                :  7.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.59
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.21
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.05
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.14
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.71
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.00
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.95
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.94
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17384.51
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.99
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.58
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.05
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.54
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.24
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.33
 p-value of test no 152                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.33
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.63
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.03
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.95
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.47
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.91
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.44
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.98
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.99
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.01
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.72
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.07
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.36
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.18
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.33
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.81
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.44
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.68
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.72
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.95
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.14
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.99
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.18
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.89
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.98
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.49
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.98
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.37
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.24
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.43
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.34
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.36
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.80
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.15
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.46
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.05
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999963443
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.30
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999868883
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.96
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.71
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35296
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 4                  :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.75
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.85
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.50
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.86
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.88
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.24
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.87
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.56
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.39
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.24
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.58
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.09
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.75
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.70
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.95
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.45
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908742
   j =  2                              :            45623
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45514
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869514
   j =  1                              :        399908975
   j =  2                              :            45508
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-4
 p-value of test no 106                :    0.9996    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.17
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.17
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.93
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.32
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.51
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.84
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.72
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.95
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.59
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.22
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.87
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.86
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.03
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.91
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.86
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.32
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.58
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.32
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  217.38
 p-value of test no 156                :  1.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.14
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.76
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.54
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.32
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.31
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.83
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   45.55
 p-value of test no 165                :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.60
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4855.13
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.62
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.34
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.12
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.42
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.62
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.47
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.58
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.13
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.95
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.85
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.95
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.36
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.80
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.18
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.52
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.98
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.22
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.97
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.99
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.39
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.22
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000035770
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.25
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999993296
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 238                :    0.81
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            0.9992 
  76  RandomWalk1 H (L=1000, r=0)     1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35297
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 3                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 9                  :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     676
 p-value of test no 31                 :  1.2e-3
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.37
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.83
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.44
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.12
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  273.87
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.13
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.32
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7251.89
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.27
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.17
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.82
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.38
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.15
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45408
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869408
   j =  1                              :        399909187
   j =  2                              :            45402
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907781
   j =  2                              :            46099
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 84                 :  1.5e-5    *****
 
 Anderson-Darling statistic = A2       :    8.05
 p-value of test no 85                 :  1.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
 p-value of test no 103                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.00
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.06
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.78
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.20
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.30
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.74
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.69
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 131                :    0.9908
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 132                :  8.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   18.85
 p-value of test no 133                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.33
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.24
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.89
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.16
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.14
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.47
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.96
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.86
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.40
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.64
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.37
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.85
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.63
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.31
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.66
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.28
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.60
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.66
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.61
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.98
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.30
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.57
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.78
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.90
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.49
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.58
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.87
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.85
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.17
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.23
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.46
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.03
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 186                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.03
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.78
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 204                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.57
 p-value of test no 207                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9985.09
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.18
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.39
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.48
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.65
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.94
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.70
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.39
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.10
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000121699
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.69
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999838796
 
 Normal statistic for number of bits   :   -1.27
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
 p-value of test no 235                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    2.11
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:30.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           7.2e-4
  47  MaxOft AD, t = 16               1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35298
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 11                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4484
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.53
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.91
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 38                 :    0.9936
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.07
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.23
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.17
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.23
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.58
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.30
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.23
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.52
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.90
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.69
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.70
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.89
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.49
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.38
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.42
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45893
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869893
   j =  1                              :        399908217
   j =  2                              :            45887
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 71                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907994
   j =  2                              :            45994
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.54
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.01
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.29
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.66
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.35
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.90
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.63
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.03
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.10
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.60
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.06
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.97
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.40
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.57
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.75
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.90
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.28
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.91
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.74
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.40
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.37
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.97
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.96
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.69
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.76
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.46
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.14
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.11
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.38
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.53
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.50
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.88
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.42
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.83
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.77
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  317.05
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.55
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.44
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.02e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.84
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.37
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.35
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.62
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.70
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.65
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.42
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.83
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.29
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.80
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.95
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.46
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.69
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000104251
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.89
 p-value of test no 233                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000078061
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 243                :    0.75
 
 Sample variance                       :    2.24
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 251                :    0.99
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:33.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35299
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5231
 p-value of test no 13                 :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4159
 p-value of test no 14                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.58
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.67
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.87
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.78
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.73
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.11
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.62
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.77
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.25
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.26
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.35
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.73
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 63                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.93
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.41
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5314.37
 p-value of test no 68                 :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908485
   j =  2                              :            45753
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907826
   j =  2                              :            46084
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.84e-4
 p-value of test no 109                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 111                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.05
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.09
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.12
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.84
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.88
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.53
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.60
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.60
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.34
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17747.17
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.76
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.49
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.41
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.36
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.42
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.24
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.56
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.59
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.20
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.34
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.85
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.87
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.34
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.32
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.34
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.14
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.66
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.42
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.01
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.84
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.01
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.29
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.67
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.14
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.39
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.08
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.04
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.20
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.24
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.69
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.32
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.76
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.28
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.91
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.037
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.61
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.13
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.41
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.44
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.42
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.41
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.74
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999911639
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.44
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000012490
 
 Normal statistic for number of bits   :   0.099
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.24
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:38.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35300
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 4                  :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.36
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    3.96
 p-value of test no 24                 :  9.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     831
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.15
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.37
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.03
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.11
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.61
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.98
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.99
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.11
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.53
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.47
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.63
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.61
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.89
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.71
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5072.78
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908094
   j =  2                              :            45947
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907521
   j =  2                              :            46238
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :   0.094
 p-value of test no 88                 : 1 -  1.2e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 97                 :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-6
 p-value of test no 113                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.46
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.14
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.25
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.53
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.07
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.58
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9980
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.83
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.36
 p-value of test no 136                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.33
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17872.28
 p-value of test no 145                :  9.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.30
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.71
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.54
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.41
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.21
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.21
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.93
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.50
 p-value of test no 154                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.88
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.55
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.65
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.40
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.10
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.70
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.15
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.53
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.11
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.40
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.50
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.67
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.53
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.24
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.87
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.10
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.06
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.16
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.97
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.67
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.85
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.00
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.39
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.66
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.55
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.20
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.30
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.55
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.48
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.60
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.53
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.27
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12114.06
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.27
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000061408
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.83
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999924470
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9962
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:58.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35301
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 5                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5398
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    2.45
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.85
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.45
 p-value of test no 41                 :  5.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.27
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.66
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.42
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.05
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.42
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.44
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.19
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.40
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.62
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.11
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.32
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.95
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908675
   j =  2                              :            45658
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908074
   j =  2                              :            45957
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 94                 :  1.7e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.79
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.12
 p-value of test no 120                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.34
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   15.39
 p-value of test no 122                :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.09
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.87
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.81
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.05
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.02
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.95
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.53
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.47
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.13
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.19
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.72
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.22
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.58
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.55
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.84
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.41
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.95
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.86
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.84
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.72
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.08
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.86
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.08
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.70
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.67
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.18
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.70
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.21
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.40
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.97
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.88
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.73
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.27
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.14
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.41
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.32
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.82
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.82
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 183                :    0.75
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.95
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.12
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.63
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.62
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.31
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.81
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.53
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4363.28
 p-value of test no 228                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.40
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.23
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.20
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000021427
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.97
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000049519
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:19.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35302
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     556
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.06
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.67
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.19
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.42
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.51
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.45
 p-value of test no 52                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.28
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.36
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.26
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.27
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.27
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.22
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.30
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.02
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.74
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907666
   j =  2                              :            46161
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908659
   j =  2                              :            45663
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.94
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.01
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.55
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.16
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.95
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.35
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.07
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.92
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.60
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.56
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.37
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.94
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.00
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.60
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.58
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.90
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.45
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.21
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.18
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.74
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.12
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.41
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.93
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.56
 p-value of test no 161                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.46
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.80
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.28
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.12
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.38
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.93
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.91
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.65
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.61
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.23
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.11
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.19
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.66
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.39
 p-value of test no 177                :  8.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.82
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.29
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.51
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.32
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.79
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.05
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.91
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.34
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.20
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.18
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.89
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.08
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000007471
 
 Normal statistic for number of bits   :   0.059
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.18
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999983135
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.07
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:07.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35303
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7521
 p-value of test no 20                 :  9.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    2.84
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.40
 p-value of test no 41                 :  6.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.69
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.76
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.61
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.39
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.38
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.21
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.62
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.41
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.81
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.64
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.76
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.00
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.52
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.22
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908050
   j =  2                              :            45969
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908650
   j =  2                              :            45666
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.03
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.72
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.38
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.21
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.79
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.69
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.62
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.05
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.62
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.14
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.55
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.72
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.37
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.06
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.73
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.57
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.62
 p-value of test no 153                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.74
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.69
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.11
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.61
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.55
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.99
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.57
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.56
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.91
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.72
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.15
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.31
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.39
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.25
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.59
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.66
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.91
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.10
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.83
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.41
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.56
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.81
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.08
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9809.84
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.57
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.66
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.07
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4307.54
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4253.62
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.69
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.58
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.82
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000201433
 
 Normal statistic for number of bits   :    1.59
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000049108
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:23.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35304
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 3                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5545
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    3.87
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.75
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.93
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.90
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.66
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.96
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.89
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.98
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.68
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.20
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.13
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.27
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.91
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   19.70
 p-value of test no 66                 :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.67
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.83
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908261
   j =  2                              :            45865
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908659
   j =  2                              :            45669
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 99                 :    0.9972
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -2.07e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.71
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.22
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.82
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.64
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.89
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.24
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.60
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
 p-value of test no 130                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.16
 p-value of test no 133                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.97
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.49
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.92
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.67
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.42
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.76
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.49
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.92
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.41
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.15
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.40
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.19
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.70
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.92
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.45
 p-value of test no 156                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.00
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.79
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.76
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.33
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.32
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.13
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.87
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.77
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.58
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.80
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.04
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.14
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.59
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.85
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.39
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.63
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.27
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.64
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.84
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.26
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.70
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.86
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.23
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.90
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 208                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10264.70
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.49
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5036.30
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.46
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.25
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.00
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.22
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.79
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.43
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999982985
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.27
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999990698
 
 Normal statistic for number of bits   :  -0.074
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 238                :    0.01
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:01.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35305
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.33
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.23
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.49
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.78
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.00
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.28
 p-value of test no 52                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.87
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.45
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.82
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1333.49
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.29
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.98
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.18
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.47
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.14
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45571
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869571
   j =  1                              :        399908863
   j =  2                              :            45561
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907797
   j =  2                              :            46097
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.38
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.14
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.52
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.63
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.45
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.33
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.91
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 142                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17707.97
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   15.96
 p-value of test no 146                :    0.9984
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.72
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.91
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.10
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.53
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.37
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.26
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.75
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.72
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.70
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.37
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.41
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.50
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.37
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.80
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.15
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.43
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.48
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.01
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.51
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.91
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.89
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.08
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.47
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.41
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.55
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.76
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.48
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.11
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.71
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.27
 p-value of test no 198                :  4.4e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.18
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.02
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.66
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.44
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.23
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.12
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.12
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.63
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.53
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12118.31
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.62
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000030910
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.44
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000012730
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:39.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35306
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 4                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    2.35
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    3.86
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.69
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.94
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.74
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.71
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.29
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.65
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.81
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.63
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.98
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.71
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.34
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.63
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.00
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.70
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908814
   j =  2                              :            45590
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908595
   j =  2                              :            45698
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9925
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.19
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.67
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.55
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.03
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.81
 p-value of test no 123                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.13
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.26
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.40
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.12
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.07
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.53
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.67
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.92
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.92
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.28
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.11
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.64
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.91
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.12
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.16
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.86
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.57
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.64
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.29
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.92
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.78
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.35
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.04
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.49
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.63
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.49
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.87
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.59
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.41
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.60
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.78
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.76
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.71
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.60
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.41
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.12
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.83
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.56
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.12
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4990.79
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.00
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.75
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.64
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12028.21
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.24
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999959006
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.28
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000132853
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.21
 p-value of test no 254                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35307
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.51
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    4.85
 p-value of test no 30                 :  3.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     657
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.76
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.05
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.95
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.43
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.05
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.67
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.18
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.91
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.96
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.46
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.66
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.34
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.47
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907852
   j =  2                              :            46068
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908718
   j =  2                              :            45638
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9912
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.76
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.64
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.17
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.11
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   69.35
 p-value of test no 123                :  1.0e-3    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.33
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.41
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.08
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.73
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.18
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17622.31
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.44
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.00
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.55
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.84
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.93
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.87
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.24
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.59
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.58
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.82
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.08
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.62
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.42
 p-value of test no 163                :  7.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.36
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.27
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.53
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.84
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.59
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.69
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.65
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.12
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.61
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.16
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.30
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.77
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.66
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.02
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9666.48
 p-value of test no 211                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.71
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.90
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.30
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.28
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.91
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.99
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12045.52
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.22
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999950474
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.99
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000044464
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             0.9994 
  63  WeightDistrib, r = 10           1.0e-3
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35308
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4450
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    2.12
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    4.04
 p-value of test no 42                 :  8.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.94
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.57
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.25
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.43
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.73
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.93
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.61
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.33
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.02
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.76
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.08
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.33
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.74
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.25
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908477
   j =  2                              :            45760
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908352
   j =  2                              :            45821
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
 p-value of test no 90                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 91                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.08
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.07
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.24
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.66
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.25
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   51.67
 p-value of test no 125                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.30
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.58
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    3.88
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   90.07
 p-value of test no 141                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16965.79
 p-value of test no 145                :    0.9939
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.25
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.57
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.21
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.11
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.14
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.40
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.62
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.03
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.02
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.48
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.55
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.96
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  562.84
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.79
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.68
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.14
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.11
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.98
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.66
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.30
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.14
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.69
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.79
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.39
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.53
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.79
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.35
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.64
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.61
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.57
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.47
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.08
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.93
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11844.68
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.23
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.20
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000026863
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.32
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999999941
 
 Normal statistic for number of bits   : -4.66e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.72
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35309
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.73
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.28
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.44
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.20
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.74
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.28
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.72
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.65
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.36
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6949.55
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.33
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.97
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.73
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.31
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.75
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908480
   j =  2                              :            45760
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907888
   j =  2                              :            46050
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-5
 p-value of test no 112                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.70
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.20
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.19
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.88
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.49
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.17
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.19
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.51
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.37
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.96
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.27
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.38
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.38
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.23
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.53
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.34
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.70
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.71
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.70
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.41
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.80
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.50
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.60
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.68
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.87
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.75
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.15
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.35
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.07
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.68
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.91
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.62
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.67
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.10
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.76
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.13
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.65
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.96
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.24
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.15
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.53
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.46
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.12
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.92
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.93
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.28
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.27
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.71
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.45
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.87
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.87
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.07
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.25
 p-value of test no 229                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.10
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.54
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000096367
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.97
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000118066
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:52.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35310
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    4.07
 p-value of test no 24                 :  8.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9968
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.00
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.79
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.16
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.84
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.92
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.22
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.61
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.86
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.70
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.54
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.72
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5205.96
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907763
   j =  2                              :            46114
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-4
 p-value of test no 112                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.85
 p-value of test no 119                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.29
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.71
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.14
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.12
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.59
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.31
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.03
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.25
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17416.51
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.94
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.13
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.01
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.94
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.73
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.97
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.17
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.98
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.21
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.24
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.49
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.43
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.00
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.40
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.58
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.36
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.47
 p-value of test no 166                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.43
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.93
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.64
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.12
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.41
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.12
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.34
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.64
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.68
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.32
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.89
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.87
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.84
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.80
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.81
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.36
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.35
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.43
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.74
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.67
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.24
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999916718
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.87
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000138418
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.97
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:37.98
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35311
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4183
 p-value of test no 14                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7476
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 27                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.33
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.11
 p-value of test no 44                 :    0.9999    *****
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.70
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.26
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.75
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.49
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.83
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.61
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.81
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.78
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.14
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.91
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.29
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.67
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.67
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.42
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908692
   j =  2                              :            45651
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46068
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870068
   j =  1                              :        399907870
   j =  2                              :            46056
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.17
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.73
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.79
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.31
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.64
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.39
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.45
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.31
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.24
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.74
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.95
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.34
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.75
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.11
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.83
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.34
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.17
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.09
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.87
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.25
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.13
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.79
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.93
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.05
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.18
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.02
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.98
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.20
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.89
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.59
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.42
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.89
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.49
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 183                :    0.01
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.28
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.09
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.17
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.77
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.78
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.09
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.19
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.87
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.71
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.36
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11878.20
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12123.79
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.69
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999974000
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.87
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999957443
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:25.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35312
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.70
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.35
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.13
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.37
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.23
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.36
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.96
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.21
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.26
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6877.16
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.94
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.56
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4891.38
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907633
   j =  2                              :            46176
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45432
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869432
   j =  1                              :        399909140
   j =  2                              :            45424
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.047
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.06
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.59
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.77
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.15
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.66
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.13
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.05
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.64
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.42
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17696.82
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.42
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.70
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.42
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.70
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.36
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.85
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.39
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.11
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.98
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.31
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.27
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.92
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.61
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.68
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.93
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.23
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.09
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.52
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.57
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.17
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  308.89
 p-value of test no 169                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.31
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.10
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.05
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.51
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.31
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.06
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.61
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.56
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 188                :    0.05
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.43
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.94
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.82
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.58
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.28
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.24
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5042.95
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.60
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.73
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.61
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.36
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.76
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000055927
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.89
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000031822
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:09.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35313
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5269
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4483
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.47
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.95
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.65
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.58
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.08
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.31
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.57
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.16
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6859.15
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.88
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.70
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.44
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.10
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.37
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908177
   j =  2                              :            45904
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.59
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.63
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.25
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.11
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.15
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.40
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.99
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.46
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.47
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17590.30
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.17
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.37
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.35
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.63
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.50
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.89
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.32
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.77
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.47
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.35
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.19
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.66
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.93
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.82
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.22
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.22
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.25
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.22
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.11
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.40
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.90
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.02
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.89
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.64
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.38
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.14
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4784.31
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.42
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.61
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.86
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.42
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.27
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.06
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.34
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.60
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.37
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.77
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.34
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.63
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.23
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.00
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.62
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.44
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000014791
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.53
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999991061
 
 Normal statistic for number of bits   :  -0.071
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 253                :    0.06
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:19.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35314
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997381
   j =  2                              :             1308
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5602
 p-value of test no 13                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 23                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 42                 :    0.9990    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 44                 :    0.9963
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.44
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.04
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.59
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.47
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.00
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.60
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.39
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.47
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.66
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.01
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.00
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.58
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.64
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.97
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45484
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869484
   j =  1                              :        399909034
   j =  2                              :            45480
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 95                 :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.02
 p-value of test no 119                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.32
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.94
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.90
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.73
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.25
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.94
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.16
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 132                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.49
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.84
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.26
 p-value of test no 136                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.89
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17534.74
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.13
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.07
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.49
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.44
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.07
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.01
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.69
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.80
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.88
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.81
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.93
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.18
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.44
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.69
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.03
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.41
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.56
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.26
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.59
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.66
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.19
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.92
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.79
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.67
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.55
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.74
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.10
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.85
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.56
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.18
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 205                :    0.9918
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.27
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.61
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.15
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.15
 p-value of test no 217                :  8.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 219                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5073.90
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 224                :  5.9e-5    *****
 
 Anderson-Darling statistic = A2       :    6.14
 p-value of test no 225                :  9.1e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5192.38
 p-value of test no 226                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.85
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.99
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.81
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11540.44
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.68
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000097627
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.63
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000052750
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:02.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP1, t = 16         0.9990 
  93  HammingCorr, L = 300            8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35315
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7544
 p-value of test no 19                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.33
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.26
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.14
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.36
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.01
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.09
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.92
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.61
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7230.42
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.66
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.49
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.78
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5125.12
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908370
   j =  2                              :            45815
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.76
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.16
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.63
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.37
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.25
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.69
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.46
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.27
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.26
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.63
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.52
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.71
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.53
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.74
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.89
 p-value of test no 152                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.12
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.60
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.99
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.50
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.02
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.45
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.14
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.03
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.17
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.57
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.25
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.26
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.64
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.27
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.37
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.45
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.97
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.42
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.40
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.97
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.74
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.11
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.77
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.29
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.08
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.22
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 219                :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 221                :  8.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4646.43
 p-value of test no 222                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.10
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.77
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.66
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.60
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.91
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.67
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999983999
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.66
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999902258
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.21
 p-value of test no 239                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:21.19
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35316
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4470
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.37
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.25
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.94
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.48
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.87
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.86
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.63
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.63
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.70
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.09
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.94
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.54
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5172.15
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46202
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907601
   j =  2                              :            46192
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45211
 p-value of test no 71                 :    0.9991    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869211
   j =  1                              :        399909581
   j =  2                              :            45205
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.90
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.30
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.92
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.09
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.29
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.69
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.14
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.47
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.97
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.55
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.90
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.00
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.79
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.01
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.69
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.70
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.04
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.97
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.04
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.95
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.46
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.78
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.84
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.09
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.22
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.27
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.47
 p-value of test no 163                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.25
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.04
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.52
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.07
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5264.29
 p-value of test no 168                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.71
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.38
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.06
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.84
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.61
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.30
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.72
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.78
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.21
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.97
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.86
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.47
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.30
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.54
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.66
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10028.55
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.72
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.88
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.50
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.72
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.55
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11946.88
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.32
 p-value of test no 231                :    0.9962
 
 
 -----------------------------------------------
 Total number of bits:  8000041095
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.75
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000108553
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 238                :    0.96
 
 Sample variance                       :    2.09
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  45  CollisionPermut, r = 10         0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35317
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997313
   j =  2                              :             1342
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.53
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.54
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.26
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.61
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.63
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.90
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.06
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.58
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.64
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7267.43
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.47
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.29
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.61
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4857.59
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45642
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869642
   j =  1                              :        399908720
   j =  2                              :            45634
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908166
   j =  2                              :            45914
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 98                 :  5.6e-3
 
 Anderson-Darling statistic = A2       :    5.08
 p-value of test no 99                 :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.02
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.46
 p-value of test no 120                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.63
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.73
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.47
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.81
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.00
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 131                :    0.9921
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.28
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.45
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17761.50
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.26
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.80
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.99
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.93
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.41
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.51
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.24
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.53
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.92
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.74
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.43
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.74
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.56
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.90
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.12
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.39
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.24
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.27
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.23
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.79
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.06
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.26
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.81
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.52
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.59
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.71
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.71
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.07
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.92
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.65
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.16
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.13
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.50
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.92
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.02
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4733.04
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.53
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.24
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.30
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12128.01
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.96
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000024862
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.82
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999990353
 
 Normal statistic for number of bits   :  -0.076
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.20
 p-value of test no 244                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:46.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35318
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 11                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 18                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.46
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.22
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.36
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.28
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.81
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.74
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.83
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.27
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.19
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.15
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.43
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.42
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.53
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908056
   j =  2                              :            45966
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908735
   j =  2                              :            45628
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.57
 p-value of test no 115                :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.12
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.57
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.44
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.27
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.70
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.24
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.87
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.94
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.66
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17084.81
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.38
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.60
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.77
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.90
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.04
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.83
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.41
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.39
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.39
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.46
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.05
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.33
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.33
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.35
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.30
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.27
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.24
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.15
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.90
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.32
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.48
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.39
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.16
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.29
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.65
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.10
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.20
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.70
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.97
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.93
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.67
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.74
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.01
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.61
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.38
 p-value of test no 216                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.01
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.88
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.16
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.88
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.30
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11354.81
 p-value of test no 230                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.46
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000038407
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.05
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000023563
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  92  HammingCorr, L = 30             0.9996 
  100  HammingIndep, L=1200, r=25      0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35319
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4507
 p-value of test no 16                 :  5.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9920
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9939
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.71
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.13
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.78
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   26.83
 p-value of test no 52                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.39
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.63
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.30
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.76
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7046.39
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.61
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.02
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.96
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.44
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.49
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908117
   j =  2                              :            45937
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908093
   j =  2                              :            45946
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-3
 p-value of test no 87                 :    0.9984
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.032
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.45
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.95
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.61
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.77
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.31
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.01
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.93
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.98
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.51
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 137                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-4
 p-value of test no 139                :    0.9991    *****
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.62
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.73
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.02
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.34
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.10
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.39
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.73
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.63
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.43
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.48
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.25
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.81
 p-value of test no 158                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.03
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.16
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.83
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.11
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.10
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.30
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.34
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.75
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.23
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.49
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  246.66
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.73
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.23
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.61
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.69
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.78
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.38
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.91
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.40
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.74
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.26
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.70
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.02
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9911
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.47
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.74
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.45
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.57
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.80
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.71
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.89
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999938891
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.16
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999892946
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.80
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:08.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35320
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.46
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.64
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.76
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.22
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.28
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.05
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.66
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.93
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.04
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.08
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.99
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.51
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.31
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5178.07
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908454
   j =  2                              :            45770
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907524
   j =  2                              :            46232
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.44e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.29
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.41
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.72
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.81
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.38
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.12
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.05
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.89
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17308.56
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.97
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.14
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.58
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.16
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.94
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.59
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.09
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.35
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.98
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.02
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.28
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.75
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.54
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.95
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.51
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.59
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.84
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.11
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.73
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.06
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.00
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.67
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.29
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.77
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.01
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.53
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.47
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.86
 p-value of test no 175                :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.52
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.17
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.36
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.47
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.50
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.31
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4693.55
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.22
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.23
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.86
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12015.19
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.67
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000033385
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.43
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999844847
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:05.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35321
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.29
 p-value of test no 40                 :  6.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.17
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.83
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.84
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.59
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.34
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.98
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1372.08
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.11
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.40
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.24
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.34
 p-value of test no 66                 :    0.9967
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.44
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5104.33
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907733
   j =  2                              :            46126
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.00
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.66
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.24
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.95
 p-value of test no 124                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.34
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.40
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.74
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  166.70
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17634.32
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.26
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.23
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.61
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.08
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.25
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.08
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.28
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.91
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.44
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.98
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.69
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.47
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.31
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.29
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.22
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.08
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.81
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.74
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.60
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.83
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.21
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.46
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.26
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.59
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.24
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.60
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.13
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.96
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.74
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.44
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.12
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.96
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 205                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 206                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.82
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.13
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.60
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 220                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5098.12
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.32
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.60
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.04
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.75
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11842.90
 p-value of test no 230                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.80
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999827279
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.76
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000066094
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:18.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35322
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5373
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7096
 p-value of test no 19                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.36
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    4.81
 p-value of test no 48                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.14
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.60
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.77
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.26
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.55
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.78
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6819.56
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.55e-3
 p-value of test no 59                 :    0.9954
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.17
 p-value of test no 61                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.39
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.26
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.86
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.48
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907978
   j =  2                              :            46002
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907824
   j =  2                              :            46082
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
 p-value of test no 73                 :    0.9965
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.52
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.29
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.21
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.31
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.24
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.14
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.90
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.69
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.52
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.88
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.16
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.00
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.17
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.06
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.95
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.35
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.92
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.86
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.11
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.84
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.69
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.67
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.65
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.47
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.53
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.49
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.13
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.33
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.40
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.86
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.61
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.55
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.99
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.69
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.84
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.42
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.22
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.91
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.58
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.70
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9920.61
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10313.46
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.85
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.54
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.96
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.46
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.47
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.37
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.40
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.40
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999961676
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.67
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999964904
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35323
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1267
 p-value of test no 6                  :    0.9959
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334387
   j =  1                              :        599997466
   j =  2                              :             1267
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 12                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4201
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.44
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.53
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.51
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.90
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.20
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.55
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.20
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  502.75
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.48
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.15
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.91
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.24
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.77
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.35
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4987.06
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45857
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869857
   j =  1                              :        399908288
   j =  2                              :            45853
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908745
   j =  2                              :            45626
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.56
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.91
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  100.66
 p-value of test no 121                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.16
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.44
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.63
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.80
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.72
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.42
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.42
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.47
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17040.97
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.30
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.71
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.31
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.67
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.29
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.88
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.55
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.83
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.51
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.24
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.73
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.74
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.42
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.79
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.72
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.35
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.04
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.43
 p-value of test no 166                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.43
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.29
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.55
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.31
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.54
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.69
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.55
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.78
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.97
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.44
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.87
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.92
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.67
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.75
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.17
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.86
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4250.08
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.33
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11964.99
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.97
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.17
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999956219
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.28
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999997493
 
 Normal statistic for number of bits   :  -0.020
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.96
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    2.22
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:36.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35324
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.47
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.30
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.80
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.16
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.27
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.96
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.73
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7296.05
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.58
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.97
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.36
 p-value of test no 66                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.68
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.33
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907941
   j =  2                              :            46022
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46278
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870278
   j =  1                              :        399907446
   j =  2                              :            46274
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
 p-value of test no 91                 :    0.9980
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.78
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.02
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.62
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.33
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.23
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.37
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.90
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.65
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.94
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.89
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.82
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.20
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.23
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.85
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.70
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.90
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.50
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.74
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.39
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.66
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.25
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.54
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.22
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.15
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.03
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.11
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.67
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.10
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.62
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.64
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.58
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.81
 p-value of test no 170                :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.72
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.69
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.30
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.05
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.76
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.36
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.00
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.96
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.98
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.61
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9716.11
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.35
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.99
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.33
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.32
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.52
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.32
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.17
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.85
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000129052
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.21
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999989315
 
 Normal statistic for number of bits   :  -0.084
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:20.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35325
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.05
 p-value of test no 29                 :  8.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     662
 p-value of test no 31                 :  6.6e-3
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.46
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.32
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.57
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.43
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.44
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.76
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.31
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.15
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.48
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.32
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.62
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.93
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5108.62
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45602
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869602
   j =  1                              :        399908797
   j =  2                              :            45600
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45757
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869757
   j =  1                              :        399908488
   j =  2                              :            45753
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.02
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.44
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.98
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.93
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.94
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 126                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.29
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.41
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.73
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.71
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.47
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.61
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.71
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.72
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.42
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.47
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.93
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.67
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.65
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.66
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.56
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.81
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.06
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.28
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.09
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.33
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.48
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.58
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.79
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.52
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.75
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.55
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.07
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.11
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.68
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.57
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.07
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.51
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    2.03
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.00
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.42
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.05
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 208                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9743.82
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.20
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.69
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.69
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.65
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.02
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.66
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.96
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.09
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000052081
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.23
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999933548
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35326
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 12                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5293
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.61
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.47
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.07
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.94
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.53
 p-value of test no 52                 :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.94
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.37
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.59
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.24
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.97
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.09
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.19
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.17
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.40
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908339
   j =  2                              :            45829
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907977
   j =  2                              :            46001
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.10
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.24
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.59
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.27
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.00
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.25
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.99
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.19
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.66
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17210.56
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.87
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.74
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.81
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.78
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.05
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.14
 p-value of test no 154                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.67
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.37
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.45
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.54
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.47
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.35
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.58
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.92
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.59
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.92
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.18
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.72
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.57
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.48
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.86
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.60
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.81
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.65
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.73
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.02
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.26
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.79
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.28
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.96
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.12
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.06
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.97
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.79
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.70
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.73
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.14
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000027742
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.88
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000052819
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 253                :    0.53
 
 Sample variance                       :    2.18
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:50.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35327
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4175
 p-value of test no 14                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    2.73
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.99
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.46
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.74
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.56
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.24
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.40
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.56
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.88
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.59
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.82
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7050.77
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.05
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.09
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.07
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.86
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908331
   j =  2                              :            45830
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908560
   j =  2                              :            45717
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.53
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.64
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.08
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.08
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.92
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.80
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.86
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.66
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.20
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17437.91
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.76
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.97
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.32
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.90
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.81
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.90
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.23
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.71
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.40
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.65
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.64
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.07
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.49
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.20
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.93
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.84
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.05
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.46
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.39
 p-value of test no 166                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.10
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.93
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.98
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.17
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.09
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.34
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.06
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.10
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.74
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.88
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.73
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.61
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.89
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.16
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.03
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 209                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9728.43
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.46
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.31
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.83
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.52
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4282.53
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.76
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.14
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.99
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999885032
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.89
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000014860
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 241                :  7.5e-4    *****
 
 Anderson-Darling statistic = A2       :    5.00
 p-value of test no 242                :  3.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.57
 p-value of test no 243                :  5.1e-3
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:55.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35328
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 10                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.66
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.99
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.34
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.41
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.95
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.50
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.99
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.91
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7272.74
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.59
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.04
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.22
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5205.48
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46182
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870182
   j =  1                              :        399907639
   j =  2                              :            46176
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.52e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.55
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.76
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.48
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.35
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.08
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.45
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.34
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.13
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  158.75
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.57
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.10
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.60
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.06
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.30
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.23
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.32
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.44
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.68
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.91
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.48
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.31
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.88
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.30
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.86
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.78
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.56
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.67
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.48
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.93
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.61
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.64
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.31
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.43
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.27
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.32
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.60
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.89
 p-value of test no 174                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.13
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.18
 p-value of test no 178                :    0.9941
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.55
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.91
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.27
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10240.54
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.21
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.78
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.34
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.22
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.42
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12128.83
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12101.05
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.34
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000038347
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.58
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000082855
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35329
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4169
 p-value of test no 17                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    4.75
 p-value of test no 42                 :  3.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     117
 p-value of test no 43                 :    0.9970
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.86
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.49
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.84
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.54
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.07
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.38
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.69
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.44
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.85
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.93
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6738.94
 p-value of test no 57                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.10
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.78
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.50
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.39
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.52
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45825
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869825
   j =  1                              :        399908354
   j =  2                              :            45817
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.60
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.78
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.35
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.46
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.67
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.72
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.42
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.78
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.06
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.09
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17170.28
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.06
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.60
 p-value of test no 147                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.57
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.54
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.40
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.77
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.76
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.51
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.37
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.44
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.86
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.71
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.49
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.59
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.95
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.10
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.29
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.61
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.60
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.68
 p-value of test no 166                :  6.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.03
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.08
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.93
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.19
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.27
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.76
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.20
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.10
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.22
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.24
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.18
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
 p-value of test no 180                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.26
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 202                :  9.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.95
 p-value of test no 203                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.68
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.83
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.59
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
 p-value of test no 219                :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5100.50
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.85
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3949.83
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.53
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.73
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12112.20
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.93
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000074230
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.92
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000070945
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9932
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.19
 p-value of test no 254                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35330
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    1.79
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.12
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.83
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.62
 p-value of test no 50                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.74
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.62
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.48
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.42
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.52
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.56
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.44
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.24
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.70
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45655
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869655
   j =  1                              :        399908691
   j =  2                              :            45653
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46295
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870295
   j =  1                              :        399907413
   j =  2                              :            46289
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.12
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.62
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.54
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.04
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.35
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.89
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.27
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.87
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.42
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.37
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.29
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.35
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.50
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.47
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.92
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.92
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.32
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.99
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.10
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.79
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.79
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.97
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.66
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.40
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.96
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.93
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.73
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.53
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.57
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.44
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.58
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.65
 p-value of test no 172                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.72
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.62
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.16
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.33
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    2.59
 p-value of test no 184                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.43
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.13
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.87
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.30
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 214                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.72
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.67
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5093.61
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.58
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.28
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.31
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11494.63
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.14
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000102766
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.46
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000157546
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.019
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35331
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 8                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     834
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.71
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.84
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.99
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.53
 p-value of test no 52                 :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.68
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.98
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.59
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.24
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.64
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.63
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.47
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.93
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45249
 p-value of test no 70                 :    0.9984
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869249
   j =  1                              :        399909504
   j =  2                              :            45245
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46314
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870314
   j =  1                              :        399907376
   j =  2                              :            46306
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.04
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.22
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.05
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.21
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.98
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.48
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.86
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.90
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.50
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.83
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.80
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.67
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.78
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.00
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.22
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.04
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.04
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.49
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.67
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.09
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.43
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.46
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.16
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.09
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.82
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.67
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.58
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.40
 p-value of test no 166                :  7.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.73
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.71
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.37
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.07
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.14
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.47
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.84
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.25
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.24
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.57
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.52
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.13
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.69
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.17
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.08
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.67
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.39e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.95
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.98
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.05
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.13
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.51
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.58
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.90
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999865121
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.44
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000014572
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    2.08
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:30.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35332
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4537
 p-value of test no 17                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.49
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.25
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.92
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.37
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.12
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.79
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.87
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.95
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  349.82
 p-value of test no 55                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.37
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.92
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.72
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.55
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.85
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.40
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.40
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45605
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869605
   j =  1                              :        399908793
   j =  2                              :            45599
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907767
   j =  2                              :            46109
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.22
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.28
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.09
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.53
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.07
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.44
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.66
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.07
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.78
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.87
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.70
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.78
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.27
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.98
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.05
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.40
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.88
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.61
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.07
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.96
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.31
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.13
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.08
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.13
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.58
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.20
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.72
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.44
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.33
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.62
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.51
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.62
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.46
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.53
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   32.15
 p-value of test no 176                :  1.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.08
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.13
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.45
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.72
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.83
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.52
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.61
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.29
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.54
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.99
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.17
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.05
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.15
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999947120
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.09
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000133891
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9915
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:14.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35333
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.28
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.18
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.20
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.72
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.25
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.75
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.10
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.58
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.56
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.10
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.60
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.10
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45796
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869796
   j =  1                              :        399908410
   j =  2                              :            45792
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45528
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869528
   j =  1                              :        399908948
   j =  2                              :            45520
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 106                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    3.83
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 117                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.79
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.73
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.52
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.37
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.93
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.48
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.38
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.65
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.35
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.75
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17652.52
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.21
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.35
 p-value of test no 148                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.54
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.69
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.34
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.13
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.56
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.27
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.93
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.68
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.24
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.33
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.71
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.04
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.66
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.72
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.69
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.95
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.98
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.59
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.15
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.97
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.81
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.96
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.71
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.17
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.17
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.23
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.46
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.42
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.33
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 204                :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  246.69
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10112.53
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.26
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.06e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4696.75
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 223                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5020.52
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.13
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.37
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12275.53
 p-value of test no 229                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.99
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.77
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000024442
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.14
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999993485
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:21.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35334
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5471
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7518
 p-value of test no 15                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.94
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.12
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.69
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.73
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.55
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.57
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.89
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.39
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6923.86
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.86
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.48
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.19
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.63
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.86
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908087
   j =  2                              :            45952
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46193
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870193
   j =  1                              :        399907618
   j =  2                              :            46185
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
 p-value of test no 86                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  8.0e-3
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  7.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.62
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.07
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.95
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.19
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.69
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.20
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.81
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.14
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17362.53
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.52
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.02
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.52
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.48
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.86
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.20
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.53
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.94
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.62
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.62
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.03
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.38
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.26
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.06
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.29
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.05
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.77
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.45
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.44
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.05
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.02
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.19
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.88
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.37
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.88
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.56
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.91
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.29
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.07
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 210                :  8.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9617.49
 p-value of test no 211                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.28
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.93
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.78
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3969.25
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.42
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.59
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12133.10
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.92
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999828791
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.18
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000039295
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:05.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35335
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 7                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.30
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.39
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.34
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.87
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.55
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.95
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.18
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.47
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1375.99
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.39
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.06
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.67
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.02
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.97
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.25
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45581
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869581
   j =  1                              :        399908843
   j =  2                              :            45571
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908107
   j =  2                              :            45942
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
 p-value of test no 106                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.50
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.33
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.14
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.78
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.47
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.91
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.61
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.95
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.98
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.90
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.79
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.06
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.74
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.66
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.77
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.87
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.43
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.81
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.91
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.46
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.55
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.23
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.95
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.67
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.59
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.58
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.33
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.41
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.27
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.29
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.15
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.64
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.57
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.07
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.99
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.32
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.98
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.73
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.16
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.87
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.32
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.03
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.65
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.06
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4263.78
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.63
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.18
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12429.35
 p-value of test no 230                :  5.5e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.90
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999949871
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.84
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999987692
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:09.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      5.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35336
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5225
 p-value of test no 13                 :    0.9962
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 24                 :    0.9993    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.48
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.50
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.84
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.85
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.78
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.15
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.50
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.09
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6900.25
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.06
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.41
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.32
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.64
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908205
   j =  2                              :            45890
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45580
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869580
   j =  1                              :        399908845
   j =  2                              :            45570
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 88                 :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.15
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.98
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.14
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.90
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.42
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.08
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.97
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.67
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.89
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.84
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.94
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.31
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.86
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.90
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.59
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.90
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.61
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.05
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.88
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.84
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.74
 p-value of test no 159                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.16
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.43
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.08
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.57
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.29
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.10
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.61
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.76
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.88
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.52
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.38
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.74
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.24
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.75
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.00
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.23
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.90
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.96
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.98
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.15
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.18
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.45
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.72
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.89
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.14
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.79
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11564.37
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.93
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999987023
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.64
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999980777
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 251                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:38.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35337
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7547
 p-value of test no 20                 :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     557
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.26
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.52
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.40
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.78
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.74
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.01
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.99
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.65
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.53
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.33
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.36
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.81
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.86
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.17
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908508
   j =  2                              :            45740
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909107
   j =  2                              :            45436
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 93                 :    0.9912
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 103                :  2.6e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    5.09
 p-value of test no 105                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.43
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.34
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.45
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.02
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.67
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.94
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.78
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.71
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.01
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.53
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.43
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.05
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.57
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.76
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.82
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.17
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.46
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.39
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.75
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.07
 p-value of test no 155                :  4.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.29
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.87
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.83
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.46
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.20
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.09
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.50
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.31
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   88.46
 p-value of test no 164                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.93
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.33
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.58
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.31
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.25
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.07
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.13
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.69
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.37
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.89
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.21
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.90
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 180                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 181                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    6.76
 p-value of test no 182                :  4.7e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.55
 p-value of test no 183                :  1.9e-4    *****
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.41
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.57
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.38
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10163.28
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.53
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.34
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.93
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.62
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.86
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.36
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.04
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000001426
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.44
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000019864
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.24
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.039
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:28.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    0.9995 
  82  LempelZiv, r = 0                1.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35338
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.89
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.46
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.65
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.96
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.41
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.73
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.37
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1499.64
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.23
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.69
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.06
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.20
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.42
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45624
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869624
   j =  1                              :        399908754
   j =  2                              :            45620
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45548
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869548
   j =  1                              :        399908907
   j =  2                              :            45542
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.29
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.98
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.63
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.01
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.34
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.12
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.14
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.67
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.99
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17420.58
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.27
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.05
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.00
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.84
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.11
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.01
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.97
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.47
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.62
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.87
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.99
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.55
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.52
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.66
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.04
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.17
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.11
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.96
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.09
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4821.52
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.25
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.80
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.39
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.72
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.90
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.83
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.68
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 188                :    0.01
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.76
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.96
 p-value of test no 203                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.36
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.67
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.76
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 220                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.70
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.48
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.65
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.76
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.23
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.91
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.93
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000021409
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.58
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999973574
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.061
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:48.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35339
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1236
 p-value of test no 12                 :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334356
   j =  1                              :        599997528
   j =  2                              :             1236
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.44
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.85
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.14
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.60
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.83
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.46
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.74
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.20
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.39
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.79
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.08
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7094.99
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.14
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.91
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.05
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.84
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5219.61
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908163
   j =  2                              :            45911
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908619
   j =  2                              :            45689
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.48
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.58
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.22
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.61
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.48
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.73
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.23
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17089.14
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.52
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.96
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.87
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.86
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.35
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.03
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.15
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.97
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.30
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.04
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.58
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.02
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.64
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.60
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.83
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.24
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.37
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   92.84
 p-value of test no 164                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.56
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.31
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.14
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.54
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.25
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.39
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.44
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.71
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.97
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.00
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.98
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.85
 p-value of test no 176                :    0.9965
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 180                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.94
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.52
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9856.27
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.27
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.07
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.11
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.06
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.86
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.65
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.54
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.35
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999973607
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.50
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999942734
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:07.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35340
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.41
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.98
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.64
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.15
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.87
 p-value of test no 53                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.47
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.60
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.73
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6742.78
 p-value of test no 57                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.98
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.57
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.25
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.67
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908352
   j =  2                              :            45815
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907879
   j =  2                              :            46053
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-3
 p-value of test no 103                :    0.9990
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 115                :  8.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.62
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.81
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.12
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.77
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.99
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.31
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.48
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.60
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.67
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.30
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.88
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17091.54
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.93
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.97
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.10
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.22
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.74
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.57
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.83
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.04
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.24
 p-value of test no 155                :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.04
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.95
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.27
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.48
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.33
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.77
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.51
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.42
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.85
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.70
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.91
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.03
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.12
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.61
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.20
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.74
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.64
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.05
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.89
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.88
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.10
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.85
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10090.69
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.63
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4688.59
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.58
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.75
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.79
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.67
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.02
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.05
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000022186
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.65
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000125152
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.89
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:25.28
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35341
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    3.90
 p-value of test no 32                 :  9.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.96
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.84
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.33
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.81
 p-value of test no 49                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.79
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.26
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.15
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.96
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.87
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.93
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7154.51
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.81
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.03
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.18
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.46
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.07
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45525
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869525
   j =  1                              :        399908952
   j =  2                              :            45521
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 111                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.81
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.28
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.31
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.43
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.79
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 130                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.52
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.32
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17132.69
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.38
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.36
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.31
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.56
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.94
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.53
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.10
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.01
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.60
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.04
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.70
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.81
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.49
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.93
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.44
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.17
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.54
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.30
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.13
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.34
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.02
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.95
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.35
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.91
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.82
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.40
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.25
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.36
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.40
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.74
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10292.61
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.55
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.87
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.88
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.40
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.93
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.95
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.07
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000083434
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.95
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999930053
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.01
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:44.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35342
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.80
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.18
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.89
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.80
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.61
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.60
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.13
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.68
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.06
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7265.25
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.57
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.28
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.25
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.18
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.87
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45973
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869973
   j =  1                              :        399908058
   j =  2                              :            45965
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908196
   j =  2                              :            45893
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.70
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.09
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.13
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.06
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.37
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.28
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.20
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.81
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.74
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.44
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17624.92
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.09
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.91
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.84
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.39
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.69
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.35
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.79
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.86
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.30
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.74
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.39
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.46
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.22
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.93
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.06
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.67
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.09
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.22
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.61
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.09
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.00
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.96
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.75
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.05
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.45
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.01
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.62
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.15
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.77
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.69
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.61
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.98
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.52
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.28
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.72
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.53
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.87
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.40
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999935405
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.10
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999931919
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    2.33
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-4
 p-value of test no 240                :    0.9990    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.20
 p-value of test no 243                :    0.01
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 245                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 246                :    0.9922
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.59
 p-value of test no 248                :    0.9953
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:23.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35343
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 5                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1238
 p-value of test no 11                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334358
   j =  1                              :        599997524
   j =  2                              :             1238
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.89
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.84
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.70
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.83
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.61
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.82
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.79
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.11
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.15
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.47
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.69
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.56
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.44
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.15
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908709
   j =  2                              :            45638
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46114
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870114
   j =  1                              :        399907778
   j =  2                              :            46102
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.76
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.45
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.73
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.87
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.96
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.46
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.89
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.71
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.68
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.64
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.31
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.11
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.21
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.51
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.63
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.78
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.13
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.25
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.80
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.97
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.08
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.81
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.50
 p-value of test no 162                :    0.9913
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.40
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.66
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.07
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.38
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4899.33
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  453.66
 p-value of test no 169                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.32
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.17
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.77
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.53
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.71
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.46
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 183                :    0.51
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.99
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
 p-value of test no 205                :    0.9983
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.53
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.69
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.66
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.16
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.41
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.13
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.51
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.85
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11666.94
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11880.28
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.32
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999972596
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.93
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999991775
 
 Normal statistic for number of bits   :  -0.065
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.88
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.92
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:09.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35344
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 7                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 10                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7056
 p-value of test no 20                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.45
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.75
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.39
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.38
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.27
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.92
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.35
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.42
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.39
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.88
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.91
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7212.82
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.76
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.81
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.64
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4865.97
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908077
   j =  2                              :            45957
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908589
   j =  2                              :            45701
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
 p-value of test no 90                 :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
 p-value of test no 97                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.91
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.82
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.27
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.73
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.47
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.65
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.14
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.89
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.07
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17592.97
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.47
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.55
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.34
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.34
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.51
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.07
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.92
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.89
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.74
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.53
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.26
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.63
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.21
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.72
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.45
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.16
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.01
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.93
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.78
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.53
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.08
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.02
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.78
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.88
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.53
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.26
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.12
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.85
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.27
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.66
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.00
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.97
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.50
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.97
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.24
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5080.31
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.38
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.24
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.14
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.12
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.35
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999957533
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.94
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999906149
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35345
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7513
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    4.29
 p-value of test no 30                 :  6.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     540
 p-value of test no 31                 :    0.9931
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.34
 p-value of test no 47                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.17
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.24
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.54
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.51
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.46
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.61
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.12
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.99
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.24
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.77
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.44
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.05
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.82
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5191.81
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908294
   j =  2                              :            45850
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45966
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869966
   j =  1                              :        399908077
   j =  2                              :            45948
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.55
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.60
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.67
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.57
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.21
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.66
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.19
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.83
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.60
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.68
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.64
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.50
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.12
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.74
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.55
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.67
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.10
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.71
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.69
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.30
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.75
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.62
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.42
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.79
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.79
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.35
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.09
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.49
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.06
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.42
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.13
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.21
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.24
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.69
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.87
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.04
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.45
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.04
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.46
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.75
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.11
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.89
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.18
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4749.44
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.69
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.86
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.21
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.39
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.14
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.04
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999928721
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.48
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999982877
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.07
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    2.18
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:48.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35346
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.79
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.30
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.46
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.12
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.33
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.44
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.53
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.61
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.62
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.68
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.74
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.89
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 62                 :    0.9933
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.37
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.31
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.96
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908495
   j =  2                              :            45748
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908307
   j =  2                              :            45839
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.56
 p-value of test no 117                :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.34
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.09
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.71
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.38
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.05
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.71
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.14
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.55
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17384.92
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.80
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.83
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.48
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.82
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.54
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.80
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.19
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.99
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.18
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.22
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.64
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.20
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.50
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.60
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.28
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.79
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.55
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.29
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.63
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.13
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.13
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.06
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.43
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.78
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.63
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.93
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.41
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.18
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.41
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.68
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    2.49
 p-value of test no 184                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 186                :    0.9905
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.53
 p-value of test no 188                :    0.9942
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.35
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.34
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 204                :  2.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.03
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.48
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.19
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.01
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.15
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.86
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.17
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.11
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.39
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.15
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.13
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999951638
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.36
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000047188
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:17.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35347
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1249
 p-value of test no 10                 :    0.9992    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334369
   j =  1                              :        599997502
   j =  2                              :             1249
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.12
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.75
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.43
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.72
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.85
 p-value of test no 50                 :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.87
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.74
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.26
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.47
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.79
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.62
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.11
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.18
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.57
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.87
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.41
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908448
   j =  2                              :            45770
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46154
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870154
   j =  1                              :        399907695
   j =  2                              :            46148
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 98                 :    0.9953
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.70
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.88
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.13
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.41
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.16
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.59
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.92
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.13
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.20
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.15
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.77
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17447.99
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.82
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.92
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.61
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.85
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.09
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.91
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.36
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.10
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.80
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.49
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.46
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.77
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.89
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.39
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.21
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.89
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.59
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5240.55
 p-value of test no 168                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.23
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.66
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.44
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.08
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.14
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.22
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.90
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.45
 p-value of test no 176                :    0.9914
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.24
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.14
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.09
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.96
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.92
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.87
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5064.79
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.02
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.29
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3950.64
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.15
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.46
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.01
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000045025
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.29
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999987905
 
 Normal statistic for number of bits   :  -0.096
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.15
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:40.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35348
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5410
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 15                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    3.00
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    3.01
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.44
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.21
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.08
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.98
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.55
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.36
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.55
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6860.51
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.58
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.31
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.46
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.37
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.81
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908452
   j =  2                              :            45771
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908400
   j =  2                              :            45797
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 93                 :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  8.5e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  3.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.65
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.69
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.03
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.19
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.08
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.35
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.16
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.53
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.03
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17633.74
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.16
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.41
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.24
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.76
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.71
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.27
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.23
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.84
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.35
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.86
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.12
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.11
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.38
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.09
 p-value of test no 164                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.38
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.76
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.25
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.08
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.44
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.07
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.56
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.28
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.45
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.76
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.56
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 188                :  9.2e-3
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.05
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.11
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9785.85
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.76
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.66
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.19
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.30
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.92
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.29
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11940.68
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.48
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999893039
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.04
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999925940
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.43
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:19.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35349
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.29
 p-value of test no 40                 :  6.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    3.53
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.09
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.88
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.81
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.81
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.92
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.38
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.86
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.02
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.80
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.16
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.18
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.08
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.88
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45872
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869872
   j =  1                              :        399908260
   j =  2                              :            45864
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908569
   j =  2                              :            45708
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.79
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.58
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.95
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.16
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.49
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.21
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.11
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.67
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.15
 p-value of test no 135                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.47
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17190.99
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.04
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.07
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.32
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.06
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.83
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.51
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.24
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.89
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.46
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.98
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.59
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.34
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.32
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.97
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.61
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.71
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.42
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.69
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.37
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5228.82
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.89
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.50
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.36
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.48
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.36
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.87
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.55
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.99
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.07
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.86
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.80
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.72
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.72
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.72
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.58
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.36
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.28
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.47
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.80
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.58
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.93
 p-value of test no 231                :  7.8e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000071089
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.07
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000010786
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35350
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     548
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.17
 p-value of test no 33                 :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.86
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.65
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.38
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.20
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.28
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.38
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  496.05
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.11
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.18
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.43
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.55
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.54
 p-value of test no 66                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.02
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.72
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908219
   j =  2                              :            45889
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908588
   j =  2                              :            45703
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.64
 p-value of test no 119                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.55
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.98
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.45
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.11
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.12
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 126                :    0.9946
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.41
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.89
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.53
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.96
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 142                :  2.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16974.25
 p-value of test no 145                :    0.9930
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.24
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.95
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.17
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.32
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.54
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.14
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.04
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.58
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.04
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.70
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.69
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.99
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.04
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.77
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.18
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.44
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.91
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.31
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.72
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.01
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.77
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.69
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.01
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.70
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.05
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.79
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.87
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.63
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.11
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.05
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.39
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.67
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.42
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.99
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.90
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10209.24
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.12
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4704.84
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 225                :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.21
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.53
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.20
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11556.97
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11542.43
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.59
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999959411
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.96
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000065686
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    2.32
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35351
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.80
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.15
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.55
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.98
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.76
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.01
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.98
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.62
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.89
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.72
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6822.02
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.41
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.78
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.49
 p-value of test no 66                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.12
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.33
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907812
   j =  2                              :            46091
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908029
   j =  2                              :            45978
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 90                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 99                 :  8.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.70
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.79
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.88
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.88
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.75
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.06
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.97
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.54
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.66
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
 p-value of test no 142                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17826.95
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.28
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.93
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.10
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.25
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.55
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.08
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.99
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.15
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.18
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.41
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.78
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.85
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.67
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.31
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.64
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.80
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.94
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.89
 p-value of test no 164                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.04
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.15
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.40
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.47
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.07
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.87
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.55
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.30
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.42
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.34
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.55
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.90
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.09
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.76
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.66
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.73
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.83
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.77
 p-value of test no 217                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.80
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.73
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.84
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.15
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11575.71
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.69
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.95
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999958826
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.44
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000176869
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:39.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35352
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997275
   j =  2                              :             1361
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.06
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.35
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.14
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.26
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.87
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.25
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.77
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.59
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.22
 p-value of test no 53                 :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.39
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.15
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.27
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7018.48
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.16
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.04
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.68
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.51
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5106.80
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46233
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870233
   j =  1                              :        399907534
   j =  2                              :            46233
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45710
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869710
   j =  1                              :        399908587
   j =  2                              :            45696
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.13
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.45
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.62
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.56
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.72
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.59
 p-value of test no 125                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.93
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.22
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.66
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17160.15
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.41
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.56
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.27
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.14
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.21
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.47
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.14
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.75
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.35
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.86
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.76
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.54
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.85
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.54
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.26
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.87
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.99
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.05
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.46
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.09
 p-value of test no 168                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.93
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.41
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.88
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.19
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.24
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.34
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  256.40
 p-value of test no 175                :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.02
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.45
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.38
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.82
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.27
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10021.46
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.39
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.81
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5102.07
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.79
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4068.07
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.55
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.89
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.35
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000043975
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.07
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999986678
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35353
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997195
   j =  2                              :             1401
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5548
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.03
 p-value of test no 34                 :  8.8e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.84
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.34
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.29
 p-value of test no 49                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.60
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.41
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.40
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.04
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.98
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.44
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.92
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.46
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.63
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.47
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.58
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.40
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.28
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908594
   j =  2                              :            45697
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45989
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869989
   j =  1                              :        399908024
   j =  2                              :            45985
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-5
 p-value of test no 87                 : 1 -  4.3e-5    *****
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9951
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.68e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.80
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.72
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.98
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.34
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.56
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.12
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.19
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.07
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.75
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.20
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.44
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.58
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.33
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.39
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.36
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.63
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.19
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.67
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.31
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.49
 p-value of test no 157                :    0.9942
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.71
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.09
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.30
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.89
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.18
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.33
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.65
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.87
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.05
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.39
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.40
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.10
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.19
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.98
 p-value of test no 171                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.97
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.68
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.94
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.27
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.93
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.22
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.87
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.21
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.67
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9834.60
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.97
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.97
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.84
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.16
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3904.58
 p-value of test no 228                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.56
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.29
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.02
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000112429
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.02
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999960824
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.9901
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.14e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:40.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35354
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 6                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    3.94
 p-value of test no 30                 :  9.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    4.74
 p-value of test no 45                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.52
 p-value of test no 47                 :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.17
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.41
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.09
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.84
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.09
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.86
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.86
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7098.07
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.71
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.00
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.45
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.98
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908566
   j =  2                              :            45711
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908579
   j =  2                              :            45703
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 100                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.11
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.98
 p-value of test no 122                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.49
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.69
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 127                :    0.9931
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.37
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.59
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.65
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.99
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.00
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.90
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.50
 p-value of test no 148                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.78
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.76
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.78
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.32
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.06
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.19
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.48
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.03
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.43
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.40
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.68
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.79
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.41
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.33
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.48
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.52
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.56
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.38
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.48
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.12
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.81
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.34
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.28
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5076.93
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.95
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.49
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.77
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.72
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.65
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.26
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.66
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.64
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.89
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.46
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.71
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.97
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3941.50
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.97
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.15
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12097.64
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.24
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000035833
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.79
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999978077
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    2.63
 p-value of test no 239                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.017
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:38.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35355
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 44                 :    0.9976
 
 Stat. AD after spacings (mNP2-S)      :    4.13
 p-value of test no 45                 :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.80
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.86
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.19
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.65
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.42
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.94
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.30
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.48
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.20
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.24
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.45
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.73
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.69
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5286.93
 p-value of test no 68                 :  7.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908884
   j =  2                              :            45552
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.21
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.50
 p-value of test no 120                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.43
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.64
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.45
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.26
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.12
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.77
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.45
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.61
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.86
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.62
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.76
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.94
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.03
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.36
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.42
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.49
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.32
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.12
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.48
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.31
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.70
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.64
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.87
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.84
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.47
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.72
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.12
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.98
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.77
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.24
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.71
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5144.88
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.37
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.14
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.05
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.20
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.12
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.91
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.22
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.48
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.67
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.94
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.75
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.75
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.56
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4720.76
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.69
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.14
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.09
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12408.41
 p-value of test no 229                :  9.3e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.37
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.91
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000031969
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.16
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999987443
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.44
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  99  HammingIndep, L=1200, r=0       9.3e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35356
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7518
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     575
 p-value of test no 31                 :    0.84
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.03
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.94
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.92
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.05
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.75
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.60
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.01
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.41
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.62
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.26
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.96
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.29
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.46
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908363
   j =  2                              :            45814
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46215
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870215
   j =  1                              :        399907573
   j =  2                              :            46209
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.40e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.078
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.47
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.95
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   83.71
 p-value of test no 122                :  1.8e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.44
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.31
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.52
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.37
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.54
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.40
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.02
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.57
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.75
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.40
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.99
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.44
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.92
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.10
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.02
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.62
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.24
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.23
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.72
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.91
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.88
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.39
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.86
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.22
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.13
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.00
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.53
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.77
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.01
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.05
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.76
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.89
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.68
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.54
 p-value of test no 198                :  5.8e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.40
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 204                :  3.0e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    6.70
 p-value of test no 206                :  5.0e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.11
 p-value of test no 207                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.94
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.33
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.87
 p-value of test no 218                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.44
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.17
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.38
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.08
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.51
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.63
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.05
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000097282
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.33
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000056875
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  62  WeightDistrib, r = 0            1.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35357
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 10                 :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.85
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.41
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.32
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.67
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.17
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.51
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.77
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.31
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.83
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.68
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7138.62
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.89
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.60
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.33
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.45
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45704
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869704
   j =  1                              :        399908597
   j =  2                              :            45694
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908256
   j =  2                              :            45866
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.78
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.31
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.34
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.78
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.96
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.32
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.48
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.08
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17135.49
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.22
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.15
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.43
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.72
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.00
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.18
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.21
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.64
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.21
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.22
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.41
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.45
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.87
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.75
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.15
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.04
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.89
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.93
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.21
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.14
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.64
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.84
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.21
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.13
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.68
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.06
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.84
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.47
 p-value of test no 174                :    0.9924
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.50
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 183                :    0.54
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.85
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.76
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.07
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9889.29
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.20
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.60
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.69
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.78
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11615.77
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.24
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.41
 p-value of test no 231                :    0.9941
 
 
 -----------------------------------------------
 Total number of bits:  8000092314
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.62
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999754832
 
 Normal statistic for number of bits   :   -1.94
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.051
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:36.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35358
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.89
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.14
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.19
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.48
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.89
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.20
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.94
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.11
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.92
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.45
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.5e-3
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 60                 :  7.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   51.54
 p-value of test no 61                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.46
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.40
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.42
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.21
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908617
   j =  2                              :            45690
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46132
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870132
   j =  1                              :        399907739
   j =  2                              :            46126
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.87
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.56
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.45
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.65
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.82
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.91
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.50
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.92
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.73
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.79
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.69
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.20
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.47
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.07
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.53
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.86
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.49
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.11
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.72
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.72
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.47
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.53
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.84
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   89.89
 p-value of test no 159                :    0.9992    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.33
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.29
 p-value of test no 161                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.93
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.79
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.95
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.82
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.54
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.92
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.49
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.76
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.18
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.33
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.89
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.61
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.85
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.86
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.63
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.58
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.27
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.68
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.72
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.99
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.00
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.48
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.38
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.79
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11678.82
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.24
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.92
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999782261
 
 Normal statistic for number of bits   :   -1.72
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.20
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000049843
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.75
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    2.39
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.17
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:06.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 R (L=1000, r=0)     0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35359
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    5.66
 p-value of test no 33                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    3.52
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.10
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.94
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.01
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.58
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.64
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.71
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.73
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.06
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.03
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.38
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.66
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.57
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.88
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.40
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908525
   j =  2                              :            45730
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45774
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869774
   j =  1                              :        399908455
   j =  2                              :            45768
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.76
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.39
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.79
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.39
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.97
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.69
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.06
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.44
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17694.31
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.57
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.35
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.73
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.86
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.82
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.66
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.68
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.12
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.60
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.45
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.85
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.26
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.45
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.55
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.31
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.04
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.67
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.61
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.19
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.57
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.51
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.73
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.86
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.89
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.25
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.96
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.77
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.35
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.85
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.31
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9945
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.83
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.86
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.05
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.46
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.24
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.85
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.93
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.20
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.28
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.50
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.13
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.76
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000061180
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.49
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999940250
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.00
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    2.29
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35360
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.62
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     941
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.17
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.03
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.18
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.00
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.98
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  371.57
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.99
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.30
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.01
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.17
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.57
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.33
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.80
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908414
   j =  2                              :            45787
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908541
   j =  2                              :            45728
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.89
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.82
 p-value of test no 120                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.37
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.85
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.39
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.07
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.85
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.88
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.30
 p-value of test no 136                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.38
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.09
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.89
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.97
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.47
 p-value of test no 149                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.66
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.65
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.67
 p-value of test no 152                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.61
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.95
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.48
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.71
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.82
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.90
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.24
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.67
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.00
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.37
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.64
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.21
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.93
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.74
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.27
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.57
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.96
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.49
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.85
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.94
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.11
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.73
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.075
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 181                :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.61
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.69
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.79
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.41
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 214                :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.58
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.31
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.47
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.26
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.98
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.48
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.57
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.06
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999905105
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.62
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999922052
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:15.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35361
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5556
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4486
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.15
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.12
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.07
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.16
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.60
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.15
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.44
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.86
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.25
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.99
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.58
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.03
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6903.64
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.99
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.88
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.44
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.73
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908512
   j =  2                              :            45738
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908178
   j =  2                              :            45902
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 72                 :  6.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.91
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.54
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.61
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.55
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.95
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.41
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.83
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.60
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.77
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.55
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.15
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.87
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.62
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.53
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.03
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.09
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.60
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.42
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.52
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.22
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.80
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.38
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.50
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.91
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.21
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.45
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.24
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.20
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.46
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.03
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.82
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.28
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.24
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.33
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.41
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.70
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.01
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.14
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.94
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.59
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.33
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.18
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.62
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.47
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9690.57
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.14
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.30
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.83
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.50
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.78
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.65
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.22
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.19
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000097297
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.05
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000054055
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:36.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35362
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 9                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 15                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.12
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.04
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.84
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.81
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.71
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.15
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.72
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.57
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.83
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.64
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.69
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.39
 p-value of test no 65                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.09
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.59
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908574
   j =  2                              :            45710
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.97
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.30
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.04
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.91
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.50
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.68
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.59
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.44
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.07
 p-value of test no 135                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.38
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17479.89
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.53
 p-value of test no 146                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.64
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.50
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.91
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.53
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.33
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.46
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.03
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.83
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.61
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.61
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.17
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.89
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.12
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.98
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.11
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.91
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.71
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.49
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.28
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.61
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.83
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.04
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.99
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.74
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.57
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.08
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.94
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.42
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10318.89
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.89
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 219                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 220                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 221                :  9.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5164.07
 p-value of test no 222                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.89
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.51
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.20
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.63
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.74
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.73
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999946922
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.92
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999947189
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
 p-value of test no 250                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  5.7e-3
 
 Anderson-Darling statistic = A2       :    4.77
 p-value of test no 252                :  3.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.09
 p-value of test no 253                :  1.0e-3
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:49.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35363
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 8                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.74
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.11
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.33
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.11
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.58
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.87
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.26
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.57
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.39
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
 p-value of test no 58                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.05
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.50
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.42
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.02
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5152.04
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908540
   j =  2                              :            45721
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908446
   j =  2                              :            45774
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 83                 :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 85                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.42
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.46
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.46
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.41
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.37
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.78
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.53
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.25
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.58
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.16
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.56
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.16
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.53
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.82
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.26
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.86
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.27
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.61
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.16
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.30
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.89
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.87
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.24
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.00
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.87
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.72
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.98
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.44
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.21
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.96
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.55
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.74
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.81
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.85
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.70
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.31
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.05
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.97
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.72
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 187                :  6.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.64
 p-value of test no 188                :    0.9958
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.54
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.43
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.59
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.15
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9700.64
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.72
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4717.23
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.78
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.03
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11720.83
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11961.69
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.64
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999851318
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.57
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000053548
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.069
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:52.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35364
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 3                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 14                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.90
 p-value of test no 28                 :  3.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     253
 p-value of test no 37                 :    0.9970
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.41
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.59
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.48
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.19
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.11
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.88
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.17
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.08
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1544.75
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7212.82
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.25
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.51
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.35
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.79
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.26
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908619
   j =  2                              :            45686
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908347
   j =  2                              :            45822
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.02
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.90
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.98
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.86
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.58
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.89
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.65
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.95
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.47
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.37
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.68
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.52
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17148.46
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.83
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.31
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.52
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.27
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.82
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.59
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.55
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.04
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.97
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.77
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.12
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.11
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.11
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.84
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.12
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.72
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.06
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.51
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.78
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.69
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.57
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.14
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.59
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.47
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.92
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.31
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.67
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.46
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.43
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.77
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.42
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.92
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.55
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.76
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.22
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.37
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.06
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.50
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.91
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.75
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.73
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.24
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000119836
 
 Normal statistic for number of bits   :    0.95
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.30
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000104167
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 236                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
 p-value of test no 246                :    0.9982
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.81
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:15.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35365
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 36                 :    0.9968
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 45                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.75
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.44
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.81
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    5.59
 p-value of test no 49                 :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.42
 p-value of test no 51                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.60
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.49
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.20
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.67
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.46
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7231.16
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.30
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.02
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.66
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.58
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.75
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46109
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870109
   j =  1                              :        399907784
   j =  2                              :            46105
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908383
   j =  2                              :            45804
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.013
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.03
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.55
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.12
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.60
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.72
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.58
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.88
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.13
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.14
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.54
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17224.81
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.93
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.58
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.85
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.54
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.58
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.06
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.81
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.36
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.44
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.75
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.23
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.39
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.20
 p-value of test no 160                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.09
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  102.39
 p-value of test no 162                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.56
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.91
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.03
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.51
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.24
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.76
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.51
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.98
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.90
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.22
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.07
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.65
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.54
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.71
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.58
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.17
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.90
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.92
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.98
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.68
 p-value of test no 217                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5033.35
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.43
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.55
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.55
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.31
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.67
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.10
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000156751
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.61
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000110365
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.37
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.55
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.60e-3
 p-value of test no 250                :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:56.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35366
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 10                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5336
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 34                 :    0.9965
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.92
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    3.34
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.06
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.68
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.01
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.41
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.88
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.06
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.30
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6757.93
 p-value of test no 57                 :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.00
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.39
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.08
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.18
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.39
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907834
   j =  2                              :            46080
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46271
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870271
   j =  1                              :        399907462
   j =  2                              :            46263
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.24
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.04
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.11
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.92
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.81
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.45
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.87
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.18
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.79
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17194.44
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.65
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.49
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.19
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.87
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.63
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.91
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.76
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.23
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.15
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.27
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.54
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.25
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.81
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.41
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.11
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.01
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.05
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.44
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.85
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.45
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4860.10
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.82
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.58
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.75
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.43
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.85
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.42
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.99
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.68
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.02
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.40
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.93
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.71
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.25
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 223                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    4.66
 p-value of test no 225                :  4.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4611.59
 p-value of test no 226                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.51
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.27
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.23
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.25
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.78
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999978227
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000010297
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:13.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35367
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7111
 p-value of test no 18                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 23                 :    0.9949
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    3.98
 p-value of test no 32                 :  9.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.51
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.88
 p-value of test no 48                 :  8.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.74
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.88
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.88
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.47
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.18
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  508.00
 p-value of test no 55                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.30
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6932.80
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.71
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.81
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.38
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.38
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.36
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45423
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869423
   j =  1                              :        399909159
   j =  2                              :            45413
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907799
   j =  2                              :            46096
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-3
 p-value of test no 86                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.3e-3
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 88                 :  8.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  2.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.069
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.47
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.76
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.81
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.61
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.14
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.87
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.08
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.33
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.28
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.19
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.47
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.61
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.08
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.38
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.16
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.49
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.29
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.77
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.67
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.33
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.52
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.34
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.24
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.73
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.33
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.18
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.43
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.67
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.59
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.78
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.25
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.49
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.06
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.21
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.53
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.23
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.39
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.21
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.46
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.15
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.03
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.22
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.31
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.09
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.53
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.50
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.52
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.55
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.80
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.49
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000119506
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   30.31
 p-value of test no 233                :    0.9962
 
 
 -----------------------------------------------
 Total number of bits:  8000032707
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.066
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:43.53
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35368
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    3.34
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.77
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.47
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.06
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.07
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.97
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.52
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.08
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.99
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.44
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.72
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.14
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.30
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.51
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.16
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.93
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.57
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907901
   j =  2                              :            46048
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908044
   j =  2                              :            45972
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.56
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.48
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.37
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.58
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.08
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.61
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.11
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.58
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.86
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.89
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.17
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.85
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.97
 p-value of test no 151                :  5.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.64
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.11
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.84
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.77
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.56
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.62
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.18
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.62
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.24
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.01
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.11
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.50
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.81
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.41
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.96
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.36
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.75
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.40
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.77
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.95
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.15
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.70
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.21
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.92
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.33
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.23
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
 p-value of test no 201                :    0.9965
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.14
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.74
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.42
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.76
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.72
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.87
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.74
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4030.19
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.37
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.92
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.73
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999962891
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.49
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999917567
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.047
 p-value of test no 243                :    0.48
 
 Sample variance                       :    2.08
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:40.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35369
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5328
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4280
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7099
 p-value of test no 15                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.54
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.32
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.96
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.75
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.97
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.91
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.08
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.41
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.44
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1560.76
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7129.70
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.01
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.95
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.10
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.42
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.31
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46009
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870009
   j =  1                              :        399907983
   j =  2                              :            46007
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907527
   j =  2                              :            46226
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.16
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.36
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.90
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.59
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.95
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.97
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.61
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.56
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.64
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.76
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.55
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.13
 p-value of test no 146                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.32
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.12
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.70
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.04
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.95
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.01
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.61
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.37
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.99
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.35
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.48
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.27
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.57
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.41
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.19
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.19
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.01
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.31
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.86
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.42
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.84
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.31
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.59
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.36
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.69
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.36
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.41
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.80
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.24
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.01
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.71
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.07
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.70
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.68
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.19
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.88
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.90
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.41
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.86
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.61
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.46
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.50
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999953351
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.65
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999912014
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35370
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4207
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.09
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.57
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.72
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.03
 p-value of test no 49                 :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.40
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.54
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.77
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.21
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.36
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1280.71
 p-value of test no 56                 :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.92
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.14
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.37
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.42
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.64
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.82
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908067
   j =  2                              :            45959
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.68
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.00
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.65
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.51
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.07
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.88
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.96
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.24
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.41
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17519.66
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.63
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.58
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.64
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.36
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.76
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.58
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.44
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.63
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.31
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.54
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.71
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.16
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.15
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.84
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.28
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.00
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.32
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.77
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.56
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.93
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.20
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.06
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.21
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.32
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.43
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.49
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.95
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.71
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.00
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.05
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.27
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.43
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.57
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.93
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.96
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.87
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.10
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.23
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.34
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.82
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.21
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11568.96
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.95
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999878813
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.86
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999766091
 
 Normal statistic for number of bits   :   -1.85
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.33
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 248                :    0.09
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35371
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 4                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4500
 p-value of test no 14                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.56
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.32
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.12
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.24
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.47
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.00
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.58
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6973.05
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.49
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.29
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.77
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.72
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.72
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908160
   j =  2                              :            45917
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 111                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.41e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.07
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.40
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.56
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.80
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.52
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.28
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.28
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.12
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.27
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.46
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.02
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.61
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.29
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.75
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.60
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.20
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.30
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.55
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.60
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.83
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.75
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.26
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.02
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.32
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.52
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.09
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.12
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.66
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.69
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.63
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.73
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.55
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.64
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.90
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.06
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.84
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.20
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.81
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 188                :    0.27
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.02
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.49
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.70
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
 p-value of test no 208                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10258.31
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10316.07
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.13
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.09
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.10
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.31
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.98
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.88
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.50
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999950840
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.45
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000080194
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:15.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35372
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5323
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.06
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.24
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.33
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.20
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.96
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.42
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.52
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.34
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6867.06
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.90
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.62
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.98
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.87
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908689
   j =  2                              :            45645
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907892
   j =  2                              :            46048
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.35
 p-value of test no 118                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.51
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.06
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.33
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.45
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.36
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.71
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.70
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 142                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17770.73
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.32
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.38
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.01
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.49
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.07
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.88
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.61
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.37
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.91
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.07
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.57
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.45
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.63
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.05
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.86
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.13
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.37
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.41
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.07
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.49
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.52
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.98
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.95
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.49
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.63
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.95
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.08
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.65
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.52
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.32
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.50
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.36
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.81
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.69
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.81
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.02
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.14
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.51
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12146.84
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.38
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.23
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999808589
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.36
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999911903
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.094
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:01.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35373
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.52
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.61
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   36.37
 p-value of test no 49                 :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.17
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.20
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.23
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.16
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.59
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.20
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.38
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7199.71
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.13
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.51
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.39
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.94
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.76
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908368
   j =  2                              :            45816
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908111
   j =  2                              :            45937
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.60
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.68
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.36
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.69
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.40
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.06
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.70
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.61
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17451.55
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.04
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.25
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.82
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.68
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.31
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.45
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.95
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.33
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.75
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.20
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.15
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.53
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.31
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.49
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.62
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.12
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.03
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.25
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.46
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.21
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.62
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.34
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.41
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.12
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.65
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.99
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.80
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.14
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.86
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.18
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.29
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.71
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.91
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.35
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.50
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.65
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.76
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.28
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000186328
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000081619
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.21
 p-value of test no 244                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
 p-value of test no 251                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35374
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7526
 p-value of test no 21                 :  7.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.30
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9970
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.26
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.31
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.41
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.19
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.76
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.80
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.82
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.06
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.46
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7097.28
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.03
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.31
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.07
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908309
   j =  2                              :            45841
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908739
   j =  2                              :            45626
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.52
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.62
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.81
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.32
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.54
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.87
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.98
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.26
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.28
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17704.23
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.56
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.72
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.13
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.46
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.23
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.44
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.61
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.55
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.54
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.47
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.74
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.81
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.03
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.90
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.85
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.93
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.08
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.97
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.96
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.88
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.52
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.45
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.78
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.35
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.54
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.07
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.13
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.98
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.042
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.09
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.81
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.75
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.98
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.41
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.81
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.79
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.93e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.80
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.59
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.00
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.80
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.41
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.29
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.30
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000097729
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.31
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999842882
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:54.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35375
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7491
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.88
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.03
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9958
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.92
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.63
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.55
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.04
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.08
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.78
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.38
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.12
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.12
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.65
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.48
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.01
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.58
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46088
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870088
   j =  1                              :        399907830
   j =  2                              :            46076
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907793
   j =  2                              :            46099
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 83                 :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 84                 :    0.9954
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 85                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.34
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.25
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.58
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.78
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.32
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.17
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.13
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.95
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.29
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.80
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.78
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17794.46
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.58
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.47
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.15
 p-value of test no 148                :    0.9962
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.82
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.33
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.35
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.18
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   99.47
 p-value of test no 157                :    0.9988
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.38
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.40
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.12
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.44
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.10
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.86
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.48
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.15
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.91
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.19
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5165.83
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.32
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.25
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.16
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.33
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.46
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.06
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.83
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.83
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.47
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    2.11
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.99
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.78
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.40
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.14
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.44
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.01
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.86
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3960.16
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.52
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.63
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.71
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.54
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000023875
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.25
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000063790
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.072
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35376
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 7                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 9                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.87
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.68
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.44
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.73
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.55
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.61
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.50
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7324.18
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.12
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.98
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.69
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.33
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.08
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908849
   j =  2                              :            45574
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45600
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869600
   j =  1                              :        399908805
   j =  2                              :            45590
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    3.32
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.06
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.23
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.89
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.82
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.67
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.42
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.11
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.37
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.67
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.82
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17408.09
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.03
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.17
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.38
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.59
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.27
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.67
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.18
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.28
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.40
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.41
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.30
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.85
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.15
 p-value of test no 162                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.28
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.01
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.55
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.76
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.20
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.77
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.17
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.90
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.21
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.03
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.45
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.94
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.79
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.48
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.23
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.06
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.09
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.88
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.98
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.99
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.77
 p-value of test no 212                :  4.1e-7    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
 p-value of test no 213                :    0.9909
 
 Anderson-Darling statistic = A2       :   14.27
 p-value of test no 214                :  1.6e-7    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9340.22
 p-value of test no 215                : 1 -  9.3e-7    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.61
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.37
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.52
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.55
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.30
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.88
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.35
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000193921
 
 Normal statistic for number of bits   :    1.53
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.64
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999921584
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9933
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.014
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  91  HammingWeight2, r = 27         1 -  9.3e-7
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35377
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 3                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 10                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5534
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     952
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9906
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.76
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.17
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.51
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.35
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.06
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.47
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.24
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.78
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.63
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.74
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.22
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.79
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.00
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.85
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46120
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870120
   j =  1                              :        399907762
   j =  2                              :            46116
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908680
   j =  2                              :            45657
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.30
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.80
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.86
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.31
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.90
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.54
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.65
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.07
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.42
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.28
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 139                :  5.6e-3
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.31
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.66
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.75
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.81
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.85
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.73
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.78
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   62.69
 p-value of test no 154                :  2.6e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.27
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.55
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.89
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.36
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.23
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.64
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.71
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.66
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.98
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.42
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.92
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.87
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5179.84
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.13
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.12
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.31
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.16
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.59
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.27
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.30
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.00
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.13
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.94
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.85
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.63
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.97
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4729.99
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4163.41
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.52
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.12
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.36
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.73
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000094129
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.77
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000035659
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      2.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35378
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7511
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9914
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.58
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.40
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.59
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.10
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.49
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.49
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.62
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1328.86
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.52
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.68
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.66
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.52
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.83
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908709
   j =  2                              :            45644
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46028
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870028
   j =  1                              :        399907949
   j =  2                              :            46018
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.25
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.21
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.14
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.71
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.15
 p-value of test no 125                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.36
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.71
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17560.12
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.46
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.67
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.19
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.67
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.48
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.42
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.96
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.04
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.86
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.11
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.62
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.76
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.18
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.56
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.53
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.23
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.71
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.24
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.46
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.09
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.04
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.16
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.66
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.22
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.89
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.26
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  306.17
 p-value of test no 174                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.02
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.05
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.39
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.75
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.94
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.65
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.11
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.03
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.19
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.28
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 224                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.44
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.23
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.02
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.11
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.02
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.37
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999894341
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.96
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000047554
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:59.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35379
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 7                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5399
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.28
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    3.42
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.67
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.49
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.21
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.23
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.33
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.60
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.54
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.36
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.17
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.79
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.13
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.08
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.36
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.40
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.46
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5069.06
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908029
   j =  2                              :            45984
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908390
   j =  2                              :            45799
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 86                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.39e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.09
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.63
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.95
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.14
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.69
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.36
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.87
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.62
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.82
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   69.64
 p-value of test no 147                :  4.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.43
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.39
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.08
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.94
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.47
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.54
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.56
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.22
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.91
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.60
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.67
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.00
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.20
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.43
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.90
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.75
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.07
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.87
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4772.01
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.52
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.73
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.45
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.48
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.44
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.62
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.28
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.12
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9964
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 188                :    0.49
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.86
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.18
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.20
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 209                :    0.01
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10292.67
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.44
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 217                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.80
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.95
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.80
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.70
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.71
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.86
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.46
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999992549
 
 Normal statistic for number of bits   :  -0.059
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.81
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999947081
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:17.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35380
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 12                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.11
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.36
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.85
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.13
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.37
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.36
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.26
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.49
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.28
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.82
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.21
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.57
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.05
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.13
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.41
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.57
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.23
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907815
   j =  2                              :            46079
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908491
   j =  2                              :            45753
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.61
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.81
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.68
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.33
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.02
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.71
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.09
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.11
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.64
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.93
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17137.88
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.22
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.92
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.29
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.44
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.22
 p-value of test no 150                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.16
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.17
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.66
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.31
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   35.25
 p-value of test no 155                :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.70
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.61
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.94
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.06
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.28
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.07
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.78
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.04
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.38
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.55
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.03
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.34
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4908.83
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.36
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.19
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.15
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.83
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.04
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.45
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.70
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.16
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.04
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.34
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.08
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.58
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.10
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4763.26
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.70
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.79
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.43
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.77
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.64
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999887294
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.19
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999871601
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:30.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35381
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 29                 :    0.9950
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    7.52
 p-value of test no 38                 :  2.0e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.10
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.44
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.07
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.76
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.84
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.25
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.85
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.96
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.60
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.32
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.65
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.22
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.10
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908714
   j =  2                              :            45640
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908671
   j =  2                              :            45660
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.34
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.99
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.87
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.83
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.75
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.30
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.24
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.06
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17692.13
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.60
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.07
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.61
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.01
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.56
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.33
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.85
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.18
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.99
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.95
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.68
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.45
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.89
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.92
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.05
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.65
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.13
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.25
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.65
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.37
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.33
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.86
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.63
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.10
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.25
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.33
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.18
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 188                :    0.93
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.48
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.65
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.31
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.24
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9695.27
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.40
 p-value of test no 216                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5069.41
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.64
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3914.75
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.29
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.36
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.52
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.25
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000160783
 
 Normal statistic for number of bits   :    1.27
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.14
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999999197
 
 Normal statistic for number of bits   : -6.35e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.17
 p-value of test no 244                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:44.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP2, t = 9          2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35382
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 12                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    3.21
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     840
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     260
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.41
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.30
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.29
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.32
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.96
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.98
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.05
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.03
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.36
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.68
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.32
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.66
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.55
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907603
   j =  2                              :            46194
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46284
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870284
   j =  1                              :        399907434
   j =  2                              :            46280
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.50
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.56
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.69
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.44
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.87
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.21
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.42
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.95
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.65
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.27
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.48
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.23
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.13
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.40
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.03
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.78
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.75
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.01
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.31
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.35
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.15
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.58
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.52
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.19
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.46
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.49
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.93
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.74
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.91
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.86
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.08
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.43
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.71
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.67
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.22
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.98
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.37
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.43
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.14
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.10
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.05
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.19
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.64
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.67
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.31
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
 p-value of test no 205                :    0.9920
 
 Anderson-Darling statistic = A2       :    3.89
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  152.45
 p-value of test no 207                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 208                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-3
 p-value of test no 209                :    0.9976
 
 Anderson-Darling statistic = A2       :    4.85
 p-value of test no 210                :  3.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9564.55
 p-value of test no 211                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.83
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.14
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.76
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.87
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.21
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.80
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.29
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.65
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000057430
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.91
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000088450
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    2.32
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:48.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  90  HammingWeight2, r = 0           0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35383
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.93
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    4.11
 p-value of test no 39                 :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.28
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.05
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.74
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.70
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.31
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.66
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.71
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.24
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.59
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.82
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.77
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.68
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.80
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.46
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908309
   j =  2                              :            45844
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908656
   j =  2                              :            45669
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 98                 :    0.9957
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.88
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.47
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.12
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.44
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.96
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.26
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.55
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.67
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.41
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.04
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17108.00
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.59
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.43
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.39
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.12
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.93
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.64
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.38
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.48
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.00
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.02
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.14
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.73
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.03
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.02
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.71
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.67
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.09
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.99
 p-value of test no 166                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.66
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.47
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.26
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.63
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.88
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.45
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.23
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.82
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.46
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.10
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.84
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.29
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.71
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.80
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.05
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.54
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.03
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 219                :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 220                :  1.7e-3
 
 Anderson-Darling statistic = A2       :    6.85
 p-value of test no 221                :  4.3e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5227.73
 p-value of test no 222                :  4.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.32
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.15
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.63
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.35
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.72
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.01
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000147379
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.79
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000020374
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:02.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  95  HammingIndep, L=30, r=0         4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35384
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.79
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.59
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.97
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.59
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.49
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.33
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.30
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7177.23
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.21
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.72
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.31
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.41
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908912
   j =  2                              :            45541
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908431
   j =  2                              :            45783
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.28e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.69
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.47
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.68
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.22
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.59
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.14
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.82
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.56
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.19
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.81
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17319.58
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.15
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.07
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.84
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.06
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.88
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.30
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.49
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.00
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.78
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.94
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.66
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.75
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.79
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.75
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.35
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.32
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.38
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.73
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.97
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.72
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.11
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.26
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.14
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.28
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.98
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.40
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.25
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.50
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.82
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.04
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.20
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.47
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.25
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.34
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.29
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.52
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3882.90
 p-value of test no 228                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.76
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.97
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.98
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999989960
 
 Normal statistic for number of bits   :  -0.079
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.54
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000056290
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
 p-value of test no 246                :    0.9965
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.73
 p-value of test no 248                :    0.9968
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:47.92
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35385
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 4                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4463
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.89
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 36                 :    0.9951
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.95
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.75
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.16
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.79
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.62
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.82
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.81
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.19
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.14
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.62
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.98
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.22
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.50
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.17
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5103.82
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908348
   j =  2                              :            45823
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908170
   j =  2                              :            45900
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
 p-value of test no 100                :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.53
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.82
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.86
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.00
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.45
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.27
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.06
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.45
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.18
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.25
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.14
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.92
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.11
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.84
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.53
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.01
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.16
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.87
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.56
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.60
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.44
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.88
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.60
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.01
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.64
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.57
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.91
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.60
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.89
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.82
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.70
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.03
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.40
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.75
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.95
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.14
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.22
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.93
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.28
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 202                :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.24
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.75
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.03
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.14
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.74
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.48
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3923.94
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.40
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.17
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.41
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.04
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000104293
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.43
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999877682
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    3.15
 p-value of test no 239                :  8.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35386
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 41                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.87
 p-value of test no 48                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.66
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.85
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.69
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.69
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.59
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.61
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.16
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6848.42
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.45
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.02
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.54
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.18
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.27
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907880
   j =  2                              :            46054
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908365
   j =  2                              :            45813
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 107                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.03
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.38
 p-value of test no 120                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.17
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.22
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.03
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.77
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.46
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17416.10
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.71
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.26
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.67
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.64
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.13
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.72
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.53
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.77
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.45
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.67
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.37
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.61
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.99
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.19
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.72
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.68
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.27
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.44
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.54
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.97
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.21
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.99
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.94
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.45
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.73
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.15
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.06
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.76
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.60
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.62
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.06
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.02
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.60
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.99
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.27
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.83
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.25
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.40
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.75
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000190732
 
 Normal statistic for number of bits   :    1.51
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.01
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000030388
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:55.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35387
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9913
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.33
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.76
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.68
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.67
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.53
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.87
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.71
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.34
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.22
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.33
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.46
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
 p-value of test no 63                 :    0.9904
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.81
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.73
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.74
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46066
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870066
   j =  1                              :        399907870
   j =  2                              :            46062
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908009
   j =  2                              :            45991
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.85
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.03
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.76
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.50
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.24
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.68
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.41
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.30
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.98
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.05
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.67
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.93
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.11
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.34
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.22
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.41
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.71
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.81
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.69
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.19
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.31
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.85
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.61
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.15
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.07
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.06
 p-value of test no 162                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.42
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.80
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.30
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.94
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.00
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.81
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.01
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.30
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.50
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.04
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.03
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.37
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.12
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.85
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.33
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 180                :  9.8e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    5.26
 p-value of test no 182                :  2.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.81
 p-value of test no 183                :    0.9975
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.53
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.70
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.60
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.86
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  1.0e-2
 
 Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
 p-value of test no 213                :    0.9953
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9653.20
 p-value of test no 215                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.74
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.55
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.89
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.51
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.39
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12089.78
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.11
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000053530
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.11
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000097639
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 238                :    0.04
 
 Sample variance                       :    3.36
 p-value of test no 239                :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    2.00
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:47.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35388
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5459
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7492
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 34                 :    0.9964
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    4.13
 p-value of test no 42                 :  7.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.63
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.09
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.21
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.45
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.70
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.11
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.59
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.33
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6955.30
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.17
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.61
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.09
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.26
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.94
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908489
   j =  2                              :            45754
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45813
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869813
   j =  1                              :        399908376
   j =  2                              :            45809
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 84                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.87
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.92
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.62
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.79
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.84
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.06
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.84
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.44
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17149.45
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.45
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.92
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.04
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.52
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.53
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.03
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.74
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.75
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.13
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.70
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.90
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.06
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.58
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.38
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.91
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.26
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.69
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.37
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.98
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.37
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.73
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.59
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.57
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.98
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.93
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.99
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.69
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  449.25
 p-value of test no 174                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.22
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.77
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.64
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    2.34
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.29
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.22
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.58
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.74
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 220                :    0.9943
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4626.16
 p-value of test no 222                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.32
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.65
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.42
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.79
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.93
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.92
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000019978
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.18
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999875699
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 251                :  1.4e-3
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :   0.086
 p-value of test no 254                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:24.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35389
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.59
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     111
 p-value of test no 43                 :    0.9995    *****
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.49
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.45
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.86
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.86
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.00
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.15
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.32
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.93
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.18
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.75
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.25
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.63
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.81
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907760
   j =  2                              :            46111
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907971
   j =  2                              :            46010
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.55
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.42
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.64
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.54
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.35
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.60
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.84
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.67
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.45
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.59
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.98
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.72
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.01
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.11
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.51
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.39
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.43
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.49
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.74
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.15
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.29
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.61
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.18
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.42
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.18
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.85
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.20
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.61
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.27
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.21
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.73
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.03
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.14
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.64
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.19
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.99
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.71
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.43
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.29
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.86
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 192                :    0.9976
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.95
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.17
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.88
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.48
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.41
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.28
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.50
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.14
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.05
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12075.63
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.12
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999991892
 
 Normal statistic for number of bits   :  -0.064
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999920852
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.099
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:23.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35390
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.11
 p-value of test no 22                 : 1 -  5.6e-5    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.26
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.35
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.65
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.81
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.32
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.27
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.88
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.38
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.62
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.74
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.27
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.27
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.47
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.38
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.69
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.14
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.19
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907951
   j =  2                              :            46020
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908631
   j =  2                              :            45680
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.21
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.43
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.26
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.31
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.68
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.79
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.86
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.95
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.82
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.54
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.18
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.09
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.12
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.30
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.64
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.78
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.24
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.56
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.69
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.10
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.83
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.01
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.50
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.41
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.77
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.13
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.67
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.28
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.64
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.90
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.54
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.27
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.66
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.03
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.13
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.91
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.44
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.11
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.23
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.82
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.10
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.33
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.86
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 208                :  7.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9717.58
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9825.37
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.44
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.79
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.72
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.14
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.74
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.71
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.79
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000021334
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.48
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999927773
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.98
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:41.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3           1 -  5.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35391
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4228
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.94
 p-value of test no 35                 :  9.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.52
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.86
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.52
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.34
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.59
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.88
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.01
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.64
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.18
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1325.42
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.83
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.65
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.91
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.62
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.89
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.28
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907999
   j =  2                              :            45990
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46253
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870253
   j =  1                              :        399907497
   j =  2                              :            46247
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.54
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.90
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.29
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.32
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.27
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.78
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.91
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.84
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.95
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17729.76
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.05
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.96
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.00
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.22
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.84
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.25
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.67
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.76
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.81
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.41
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.40
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.15
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.81
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.89
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.30
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.20
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.68
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.00
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.82
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.21
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.81
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.38
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.98
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.33
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.32
 p-value of test no 172                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.34
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.53
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.71
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.32
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.11
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.88
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.62
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9914.62
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9765.15
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.94
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.74
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.45
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.71
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.28
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.48
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.85
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000095578
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.73
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999958415
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:07.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35392
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 11                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5542
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7140
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.00
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.13
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.91
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.21
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.86
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.45
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.09
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.76
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.56
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.75
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.93
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.52
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.10
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.07
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45724
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869724
   j =  1                              :        399908557
   j =  2                              :            45714
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908409
   j =  2                              :            45788
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.24
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.85
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.23
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.62
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.08
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.26
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.37
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.07
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.12
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  : 8.05e-3
 p-value of test no 134                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.16
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.48
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.27
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.47
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.85
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.28
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.93
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.40
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.49
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.40
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.76
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.32
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.77
 p-value of test no 155                :    0.9946
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.31
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.61
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.70
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.13
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.25
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.45
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.26
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.66
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.43
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.58
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.22
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.93
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.11
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.01
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.25
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.80
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.32
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.84
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.89
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.23
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.98
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.69
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.80
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.37
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.65
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 218                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.35
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.46
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.42
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.77
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.39
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.97
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.25
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999890078
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.70
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999993278
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.41
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 253                :    0.25
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:40.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35393
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 5                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5245
 p-value of test no 13                 :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.15
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.36
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.88
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.16
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.32
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.68
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.88
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.54
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.71
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.18
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.71
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.67
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.66
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.00
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.06
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.55
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.60
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907734
   j =  2                              :            46130
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908644
   j =  2                              :            45672
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    5.63
 p-value of test no 81                 :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  2.1e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.55
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.58
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.35
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.41
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.16
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.26
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.14
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.46
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.98
 p-value of test no 136                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  171.90
 p-value of test no 141                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17515.75
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.01
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.23
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.98
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.93
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.12
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.01
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.49
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.27
 p-value of test no 156                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.63
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.74
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.61
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.04
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.10
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.13
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.83
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.75
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.20
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.98
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.93
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4763.32
 p-value of test no 168                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.99
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.56
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.65
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.68
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.98
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.36
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.23
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.84
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.77
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.47
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.75
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.34
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.76
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.32
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.36
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4671.64
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.84
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.40
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11673.10
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.02
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999887468
 
 Normal statistic for number of bits   :   -0.89
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.01
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000041785
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:01.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft, t = 16                  2.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35394
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.28
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    3.30
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.34
 p-value of test no 48                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.03
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.75
 p-value of test no 51                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.33
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.77
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.46
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7321.18
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.08
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.95
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.52
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.08
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908049
   j =  2                              :            45968
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45467
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869467
   j =  1                              :        399909068
   j =  2                              :            45463
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  5.8e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.21
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.97
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.55
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.13
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.28
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   50.28
 p-value of test no 125                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.19
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.53
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.97
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.19
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.96
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.66
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.68
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.83
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.20
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.86
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.48
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.53
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.85
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.13
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.78
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.17
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.62
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.68
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.66
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.77
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.49
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.41
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.28
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.64
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.88
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.67
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.71
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.93
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.55
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.41
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.78
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.66
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.31
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10115.32
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.14
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.06
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.85
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.25
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.48
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.74
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12080.34
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.94
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999877961
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.43
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000186022
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 238                :    0.44
 
 Sample variance                       :    2.00
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:55.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35395
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4168
 p-value of test no 14                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.72
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.80
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.50
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.82
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.06
 p-value of test no 53                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.82
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.60
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.80
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6796.32
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.26
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.70
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.51
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.77
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.02
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907851
   j =  2                              :            46070
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46117
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870117
   j =  1                              :        399907768
   j =  2                              :            46113
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.56
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.49
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.71
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.80
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.72
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.89
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.24
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.88
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.26
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.09
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.08
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17756.17
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.51
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.28
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.34
 p-value of test no 148                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.04
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.14
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.64
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.81
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.11
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.95
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.45
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.64
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.21
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.83
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.68
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.94
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.87
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.18
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.10
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.36
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.29
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.54
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.21
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.90
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.88
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.54
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.70
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.74
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.92
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.30
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.62
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   30.35
 p-value of test no 178                :  2.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.90
 p-value of test no 179                :  4.8e-5    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.58
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.81
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-4
 p-value of test no 201                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.34
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.01
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.10
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.57
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 5.96e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 219                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.27
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.37
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3966.18
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.58
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12214.97
 p-value of test no 229                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11571.31
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.85
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000069328
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.42
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000012967
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:18.19
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 29              4.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35396
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    4.22
 p-value of test no 33                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    5.64
 p-value of test no 38                 :  1.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.25
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.29
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.96
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.75
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.51
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.64
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  507.56
 p-value of test no 55                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.49
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.44
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.44
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.77
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.03
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.73
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5255.62
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45488
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909028
   j =  2                              :            45480
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46023
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870023
   j =  1                              :        399907955
   j =  2                              :            46021
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.75
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.76
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.80
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.58
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.39
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.54
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.80
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.72
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.74
 p-value of test no 133                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.53
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.58
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17195.63
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.63
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.85
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.09
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.98
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.04
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.95
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.24
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.03
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.22
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.63
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.30
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.03
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.51
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.17
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.14
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.96
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.18
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.51
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.48
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.61
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.92
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.18
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.53
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.07
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.91
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.07
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.36
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.64
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.04
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 183                :    0.94
 
 Sample variance                       :    2.21
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.31e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.61
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.43
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.10
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.02
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.24
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.03
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5058.79
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.62
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4294.51
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3887.79
 p-value of test no 228                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11437.47
 p-value of test no 229                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12054.72
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.77
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999965930
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.79
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000040582
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.017
 p-value of test no 243                :    0.49
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:22.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35397
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 9                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.36
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.27
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.92
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.71
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.51
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.69
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.33
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.03
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.28
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6759.23
 p-value of test no 57                 :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.95
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.59
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.78
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.58
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4866.29
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908186
   j =  2                              :            45898
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908440
   j =  2                              :            45771
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.88
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.14
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.35
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.42
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.44
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.71
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.71
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.01
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.83
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.07
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.02
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.87
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.73
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.92
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.90
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.62
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.00
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.99
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.79
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.40
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.69
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.05
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.16
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.00
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.62
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.06
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.28
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.50
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.73
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.92
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.48
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.17
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.55
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.97
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.25
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.22
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.91
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  4.8e-3
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.92
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.27
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.12
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.97
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.38
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.89
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.85
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.59
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.09
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.03
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.24
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999921764
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.64
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000091657
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:24.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35398
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4505
 p-value of test no 16                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.58
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.81
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.02
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.77
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.85
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.54
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.89
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.45
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.30
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.31
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.28
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.77
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.38
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.97
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.60
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46275
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870275
   j =  1                              :        399907454
   j =  2                              :            46267
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45555
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869555
   j =  1                              :        399908892
   j =  2                              :            45551
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.71
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.58
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.70
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.37
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.33
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.48
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.01
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.39
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.49
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.19
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.38
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.16
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.31
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.15
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.70
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.39
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.50
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.63
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.48
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.50
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.35
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.26
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.20
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.02
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.62
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.13
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.04
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.22
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.75
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.64
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.14
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.67
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.67
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.17
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.10
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.71
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.45
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.24
 p-value of test no 173                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.26
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.80
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.93
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.10
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.40
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 185                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.77
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.02
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.40
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.94
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.28
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.47
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.87
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4218.78
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.56
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.12
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.23
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.16
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999837323
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.19
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000020623
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:45.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35399
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.63
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.87
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.46
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.96
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.04
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.66
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.06
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.71
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.12
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.33
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.45
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4830.04
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907770
   j =  2                              :            46115
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46000
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870000
   j =  1                              :        399908003
   j =  2                              :            45994
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 104                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.61
 p-value of test no 119                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.38
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.16
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.98
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.13
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.27
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.98
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.69
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.07
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.64
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.35
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.21
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.50
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.29
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.94
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.94
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.82
 p-value of test no 151                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.52
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.06
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.61
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.09
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.67
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.29
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.71
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.71
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.75
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.71
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.50
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.96
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.48
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.00
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.84
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.04
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.79
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.45
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.12
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.64
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.90
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.65
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.75
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.75
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.00
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 180                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.38
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.30
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.16
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.12
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.59
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.53
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 220                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.85
 p-value of test no 221                :  1.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5186.33
 p-value of test no 222                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.81
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4410.39
 p-value of test no 227                :  7.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3892.28
 p-value of test no 228                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.06
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.55
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.81
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000012730
 
 Normal statistic for number of bits   :    0.10
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.12
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000034990
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:48.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  97  HammingIndep, L=300, r=0        7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35400
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9944
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 44                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.54
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.40
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.33
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.45
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.32
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.16
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.20
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.75
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7122.53
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.93
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.84
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.39
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.92
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4920.27
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907691
   j =  2                              :            46144
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908198
   j =  2                              :            45889
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.51
 p-value of test no 115                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.45
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.36
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.34
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.86
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.66
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.59
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.45
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.07
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.78
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.83
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.79
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.99
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.80
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.36
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.82
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.13
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.54
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.63
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.24
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.87
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.44
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.70
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.34
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.62
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.86
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.58
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.48
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.39
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.44
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.60
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.03
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.49
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.54
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.91
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.54
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.37
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.37
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.34
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.33
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.68
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.88
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.54
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.70
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.74
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.12
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.09
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.50
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.64
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.26
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.98
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.88
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999914018
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.18
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000111604
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.095
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:01.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35401
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.92
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.38
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.11
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.28
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.93
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.57
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.46
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.85
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.48
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6944.65
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.50
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.20
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.88
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.95
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.34
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908101
   j =  2                              :            45939
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46194
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870194
   j =  1                              :        399907617
   j =  2                              :            46184
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 97                 :  7.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.01
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 106                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.01
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.02
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.21
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.79
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.66
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.73
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.25
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.24
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17521.43
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.80
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.13
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.59
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.60
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.31
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.52
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.07
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.96
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.94
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.37
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.18
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.79
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.52
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.38
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.82
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.65
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.00
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.25
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.05
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.35
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.81
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.55
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5065.13
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.22
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.26
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.15
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.42
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   24.25
 p-value of test no 198                :  2.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.37
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.38
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10240.55
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10298.51
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.40
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.85
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.19
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.42
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.70
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.61
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.30
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000166327
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.18
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999962069
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.22
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 247                :    0.9922
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:23.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35402
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 5                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.67
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.13
 p-value of test no 40                 :  8.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.26
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.46
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.68
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.31
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.46
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1467.85
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.37
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.25
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.23
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.84
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.84
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908396
   j =  2                              :            45799
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908665
   j =  2                              :            45666
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.43
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.05
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.57
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.70
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.35
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.77
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.33
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.94
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17468.97
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.96
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.29
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.05
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.38
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.71
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.41
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.87
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.57
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.44
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.11
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.79
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.36
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.29
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.57
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.27
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.45
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.56
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.80
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.92
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.83
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.36
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.54
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.51
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.59
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.25
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.51
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.66
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.53
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.02
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.09
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 204                :    0.9908
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.59
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.86
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 214                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.44
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5022.01
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4799.10
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.20
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.01
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.27
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.43
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.18
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999945092
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.10
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000026356
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.30
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    2.44
 p-value of test no 249                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 253                :    0.47
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35403
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 4                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 20                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.15
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.51
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.97
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.69
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.19
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.68
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.67
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.52
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.60
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.99
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.78
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.07
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.57
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.06
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.61
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.11
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908149
   j =  2                              :            45915
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907815
   j =  2                              :            46085
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 94                 :    0.9955
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.98
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.89
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.50
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.27
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.52
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.09
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.53
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.61
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.85
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.33
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17540.08
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.75
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.38
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.48
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.53
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.68
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.63
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.27
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.50
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.46
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.55
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.90
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.94
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.36
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.09
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.43
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.29
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.72
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.65
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.38
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.26
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.61
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5245.41
 p-value of test no 168                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.52
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.69
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.54
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.05
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.56
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.33
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.50
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.21
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.32
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.32
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  159.26
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.50
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.24
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.51
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.92
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.85
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.43
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.83
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12227.50
 p-value of test no 230                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.04
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000069733
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.70
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000085297
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.87
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:02.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35404
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 14                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.00
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.94
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.45
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.12
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.01
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.68
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.11
 p-value of test no 55                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.02
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.91
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.35
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.33
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.84
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5179.78
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907613
   j =  2                              :            46189
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908045
   j =  2                              :            45973
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.15
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.36
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.42
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.83
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.68
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.92
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.98
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.54
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.90
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.51
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.05
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.83
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.50
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.62
 p-value of test no 149                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.31
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.90
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.19
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.67
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.31
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.46
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.52
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.10
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.54
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.86
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.59
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.98
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.57
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.21
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.28
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.78
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.93
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.80
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.64
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.44
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.59
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.77
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.34
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.91
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.30
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.06
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 188                :    0.22
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.42
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 202                :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.20
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.14
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.01
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10255.10
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.86
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.44
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.70
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.86
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.99
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.82
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.90
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000027553
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.52
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999781703
 
 Normal statistic for number of bits   :   -1.73
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:58.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35405
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7544
 p-value of test no 21                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 22                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.77
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.37
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.31
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.55
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.67
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.21
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.10
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.35
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.38
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1549.14
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.07
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.97
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.83
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.20
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.91
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.75
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908424
   j =  2                              :            45782
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908283
   j =  2                              :            45851
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.24
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.87
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.92
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.17
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.08
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.37
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.36
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.96
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.32
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.04
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17154.63
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.82
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.75
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.17
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.26
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.27
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.68
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.10
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.63
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.76
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.16
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.29
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.91
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.52
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.56
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.37
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.27
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.88
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.80
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.29
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.28
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.01
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.06
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.68
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.08
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.03
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.92
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.69
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.85
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.01
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    2.84
 p-value of test no 184                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.76
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.92
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.04
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.15
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.43
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.09
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 225                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.42
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.66
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.28
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.01
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.91
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.96
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000001639
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.67
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000099124
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.062
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.16
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:23.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35406
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7536
 p-value of test no 18                 :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7544
 p-value of test no 19                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7515
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.09
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   24.97
 p-value of test no 47                 :  7.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.63
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.68
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.23
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.36
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.99
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.45
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.69
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.79
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.72
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.83
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 62                 :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    4.80
 p-value of test no 64                 :  3.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.52
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.36
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.84
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.91
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908051
   j =  2                              :            45970
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45402
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869402
   j =  1                              :        399909200
   j =  2                              :            45394
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.83
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.27
 p-value of test no 120                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.53
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.13
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.76
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.94
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.51
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.53
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.10
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.92
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.76
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.95
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.68
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.80
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.33
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.04
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.98
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.39
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.53
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.91
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.41
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.16
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.93
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.97
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.65
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.29
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.18
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.58
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.08
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.39
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.00
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.21
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.67
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.39
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.66
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.35
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.63
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.45
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.94
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.92
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.43
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.48
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.74
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.48
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.01
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.76
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.77
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.54
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.07
 p-value of test no 218                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
 p-value of test no 219                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    4.37
 p-value of test no 221                :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5193.97
 p-value of test no 222                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.12
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.13
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.05
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11552.40
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11639.12
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999994595
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.59
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000024259
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:46.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  27  SimpPoker, r = 27               7.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35407
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 3                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5269
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.82
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.16
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.07
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.92
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.76
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.30
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.78
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.29
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1326.53
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.30
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.90
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.86
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.62
 p-value of test no 66                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.97
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.12
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908546
   j =  2                              :            45724
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.28
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.99
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.55
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.90
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.37
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   56.57
 p-value of test no 125                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.64
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.60
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.33
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.27
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.65
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.90
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.47
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.73
 p-value of test no 150                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.45
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.64
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.10
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.48
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.55
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.52
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.99
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.77
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.99
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.32
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.95
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.75
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.94
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.58
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.81
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.02
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.46
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.27
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.39
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.07
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.51
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.59
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.42
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.11
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.06
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 183                :    0.56
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.34
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 204                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.23
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.25
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.04
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.95e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 220                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.63
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.31
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.70
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.41
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.17
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.16
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.77
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000091372
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.41
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000005140
 
 Normal statistic for number of bits   :   0.041
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:52.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35408
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 7                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.37
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.85
 p-value of test no 49                 :  8.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.27
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.70
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.31
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.07
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.74
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.36
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.08
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.51
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.16
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.91
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.92
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907995
   j =  2                              :            45998
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908267
   j =  2                              :            45859
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 72                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.29
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.26
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.39
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.90
 p-value of test no 123                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.07
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.04
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.83
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.06
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.44
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17724.42
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.60
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.53
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.44
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.95
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.99
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.44
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.07
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.25
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.56
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.94
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.46
 p-value of test no 157                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.05
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.28
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.97
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.52
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.78
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.77
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.48
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.02
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.66
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.42
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.73
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.60
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.70
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.64
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.75
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.25
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.64
 p-value of test no 174                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.39
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.05
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.95
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.43
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.54
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.49
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.79
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.31
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.93
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.80
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.89
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.80
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.03
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.51
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000048865
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.94
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999905942
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.37
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  29  SimpPoker, r = 25               8.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35409
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.05
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.10
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.73
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.07
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.48
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.32
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.14
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.06
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7076.73
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.66
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.74
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.78
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.10
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46283
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870283
   j =  1                              :        399907438
   j =  2                              :            46275
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907982
   j =  2                              :            46003
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.82
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.06
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.94
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.42
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.10
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.21
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.59
 p-value of test no 125                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.75
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.10
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.03
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17438.17
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.90
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.38
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.60
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.90
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.47
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.36
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.34
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.16
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.00
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.79
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.53
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.50
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.18
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.05
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.99
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.80
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.07
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.38
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.10
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.51
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.11
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.65
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.37
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5110.21
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.88
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.84
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.46
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.09
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.14
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.45
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.14
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.16
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.91
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.07
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4756.67
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.09
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.06
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.40
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.41
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.55
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999952073
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.39
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999890276
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:46.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35410
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.21
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.09
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.40
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.90
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.76
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.64
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.77
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.63
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.80
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.62
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.98
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7217.21
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.38
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.59
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.13
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.79
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.92
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45699
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869699
   j =  1                              :        399908604
   j =  2                              :            45695
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45343
 p-value of test no 71                 :    0.9939
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869343
   j =  1                              :        399909316
   j =  2                              :            45339
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.89
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.29
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.65
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.22
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.59
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.77
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.63
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.02
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.44
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.02
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.76
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.58
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.57
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.89
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.82
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.31
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.22
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.04
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.87
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.58
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.67
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.41
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.10
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.05
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.75
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.16
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.14
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.61
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.79
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.27
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.12
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.94
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.64
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.13
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.11
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.96
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.23
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.37
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.46
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.62
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.94
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.96
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.13
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.33
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.13e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.11
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.91
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.78
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.80
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.52
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.65
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.09
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000010807
 
 Normal statistic for number of bits   :   0.085
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.92
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000012604
 
 Normal statistic for number of bits   :   0.100
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 1.92e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.30
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35411
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7595
 p-value of test no 15                 :  6.6e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.15
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.74
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.23
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.75
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.67
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.52
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1388.32
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.86
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.62
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.92
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.74
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.46
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907611
   j =  2                              :            46190
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908372
   j =  2                              :            45811
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 117                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.37
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.51
 p-value of test no 120                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.86
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.92
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.74
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.54
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.71
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.65
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.04
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.15
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.95
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.32
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.59
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.13
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.37
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.34
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.66
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.83
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.78
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.14
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.80
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.79
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.54
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.39
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.96
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.57
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.51
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.32
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.64
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.22
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.68
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.10
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.55
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.96
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.17
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.49
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.17
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.98
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.96
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.16
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.95
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.55
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.46
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.05
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10200.68
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.74
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.22
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.64
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.83
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11894.67
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.60
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.81
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999952724
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   95.60
 p-value of test no 233                :  4.2e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  8000098134
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.65
 p-value of test no 243                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:11.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         6.6e-4
  102  Run of bits, r = 27             4.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35412
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    3.22
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    3.63
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     519
 p-value of test no 31                 :    0.9996    *****
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.54
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.67
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.15
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.65
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.59
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.44
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.79
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.68
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.54
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.81
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.28
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.62
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.14
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45806
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869806
   j =  1                              :        399908391
   j =  2                              :            45800
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908542
   j =  2                              :            45717
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.08
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.54
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.26
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.33
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.69
 p-value of test no 124                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.47
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.96
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.78
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.14
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17227.90
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.82
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.70
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.86
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.09
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.06
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.56
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.46
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.21
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.49
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.27
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  440.38
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.12
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.62
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.80
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.39
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.97
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.39
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.32
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.76
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  313.60
 p-value of test no 167                :    0.9964
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.46
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.39
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.56
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.91
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.59
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.53
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.46
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.19
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.28
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.51
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.27
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.59
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.71
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.78
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 204                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.48
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 209                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    4.94
 p-value of test no 210                :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10426.88
 p-value of test no 211                :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.70
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.74
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4711.62
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4224.54
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.13
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.85
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.48
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.35
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000230077
 
 Normal statistic for number of bits   :    1.82
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.05
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000055261
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:23.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35413
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9945
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.65
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.38
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.19
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.19
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.34
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.27
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.87
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1562.41
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7109.02
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.69
 p-value of test no 58                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.08
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.37
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.93
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.19
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4871.15
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908560
   j =  2                              :            45717
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908184
   j =  2                              :            45905
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.66
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.87
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.07
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.21
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.36
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.11
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.23
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.76
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.68
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.35
 p-value of test no 141                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17733.35
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.00
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.78
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   40.58
 p-value of test no 150                :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.99
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.69
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.86
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.60
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.94
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.17
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.00
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.98
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.30
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.78
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.91
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.19
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.77
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.89
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.40
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.57
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.94
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.08
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.31
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.37
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.45
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.52
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.66
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.18
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.29
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.23
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 192                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.02
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.87
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.26
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.64
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.52
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.49
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.14
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.77
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.56
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3926.04
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.85
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11889.31
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.83
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000034294
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.95
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000063796
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.28
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 243                :    0.27
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:44.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35414
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.08
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.03
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.16
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.05
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.70
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.01
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.56
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.75
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.46
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.45
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.32
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.67
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.62
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.19
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908145
   j =  2                              :            45923
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907709
   j =  2                              :            46141
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9937
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.40
 p-value of test no 119                :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.09
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.30
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.02
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.32
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.10
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.98
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.48
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.14
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.28
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.24
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.71
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.33
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.65
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.21
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.01
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.08
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.73
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.57
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.04
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.68
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.63
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.67
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.93
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.56
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.76
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.01
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.64
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.88
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.99
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  150.50
 p-value of test no 170                :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.48
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.09
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.46
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.52
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.24
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.69
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.31
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.73
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.81
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.47
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.86
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.91
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.75
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.74
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.83
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.54
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.50
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.54
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000062398
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.69
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999937322
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.89
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
 p-value of test no 250                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:05.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35415
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.15
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.92
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.71
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.78
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.59
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.68
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.87
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.40
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.39
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.76
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.14
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.54
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.78
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.89
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.82
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907968
   j =  2                              :            46010
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-4
 p-value of test no 112                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.57e-6
 p-value of test no 113                :    0.9988
 
 Anderson-Darling statistic = A2       :    5.03
 p-value of test no 114                :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.33
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.00
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.14
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.32
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.13
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.18
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.51
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.87
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.85
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.27
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.37
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.21
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.72
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.01
 p-value of test no 149                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.32
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.30
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.12
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.26
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.52
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.80
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.44
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.47
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.20
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.22
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.89
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.77
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.35
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.11
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.97
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.17
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.77
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.26
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.91
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.52
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.58
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.37
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.23
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.06
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.42
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.96
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.80
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.36
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.64
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.42
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.22
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.84
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.01
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.92
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.51
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.75
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11572.63
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.01
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999931922
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999977123
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    2.05
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 251                :    0.9947
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:46.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35416
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4474
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 22                 :    0.9972
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    3.23
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.18
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.28
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.86
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.43
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.71
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.97
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.54
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.18
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1473.85
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.53
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.13
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.73
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.47
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.35
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46025
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870025
   j =  1                              :        399907955
   j =  2                              :            46015
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46421
 p-value of test no 71                 :  5.8e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870421
   j =  1                              :        399907162
   j =  2                              :            46413
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 106                :    0.9903
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.83
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.34
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.47
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.81
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.43
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.21
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.12
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.94
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.42
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.39
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.68
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.01
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.08
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.88
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.35
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.06
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.80
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.55
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.72
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.99
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.37
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.17
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.42
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.34
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.04
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.82
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.07
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.20
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.15
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.65
 p-value of test no 167                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4835.27
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.45
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.40
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.87
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  458.60
 p-value of test no 172                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.21
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.20
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.41
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.92
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.21
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.68
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.45
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.19
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.24
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.97
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.26
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.20
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.23
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.31
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11963.31
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.98
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.95
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999951719
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.04
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999800501
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 236                :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.58
 p-value of test no 238                :    0.9950
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:03.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35417
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 4                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.16
 p-value of test no 46                 :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.64
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.49
 p-value of test no 48                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.53
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.80
 p-value of test no 50                 :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.01
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.76
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.16
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.90
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.71
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.49
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.21
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.93
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.24
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  169.99
 p-value of test no 67                 :  1.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.85
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908024
   j =  2                              :            45982
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907920
   j =  2                              :            46037
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 98                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.42
 p-value of test no 99                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.12
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.32
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.99
 p-value of test no 123                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.74
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.99
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.73
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.26
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.96
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.08
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.58
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.26
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.58
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.78
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.16
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.30
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.48
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.45
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.52
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.03
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.92
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.87
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.28
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.55
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.06
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.56
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.95
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.59
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.91
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.34
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.35
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.44
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.10
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.17
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.84
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.43
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.64
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.76
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.071
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.25
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.44
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.80
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.36
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.59
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.52
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.93
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.69
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.19
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.34
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11554.43
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.47
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999896246
 
 Normal statistic for number of bits   :   -0.82
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.05
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999922421
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.45
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    1.39
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:28.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35418
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.78
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.34
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.43
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.60
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.37
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.57
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.79
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.93
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.18
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.75
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.26
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.67
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.31
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.16
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.50
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908534
   j =  2                              :            45727
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908465
   j =  2                              :            45766
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
 p-value of test no 90                 :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.46e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.35
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.42
 p-value of test no 121                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.00
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.88
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.63
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.35
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.62
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.17
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 143                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17841.58
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.46
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.89
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.63
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.89
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.76
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.66
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.21
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.69
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.45
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.21
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.42
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.74
 p-value of test no 157                :    0.9950
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.14
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.97
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.50
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.94
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.77
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.68
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.65
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.60
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.95
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.51
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.34
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.50
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.71
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.26
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.11
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.92
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.05
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.82
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.88
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 183                :    0.20
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.36
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.06
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.64
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.73
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.62
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.17e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5030.21
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.60
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.80
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.28
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11838.29
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.75
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.91
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000030514
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999874508
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:39.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35419
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.05
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.93
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.23
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.21
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.21
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.70
 p-value of test no 53                 :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.37
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.79
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.32
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.43
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.80
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.63
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.13
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.97
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.13
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46135
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870135
   j =  1                              :        399907734
   j =  2                              :            46127
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908042
   j =  2                              :            45976
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.98
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.43
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.10
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.61
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.01
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.48
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.64
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.29
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.23
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.80
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.25
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.27
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.61
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.33
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.41
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.06
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.30
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.28
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.59
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.28
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.14
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.46
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.75
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  426.67
 p-value of test no 163                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.05
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.46
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.50
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.45
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.16
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.97
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.41
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  319.44
 p-value of test no 171                :    0.9929
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.74
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.39
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.21
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.52
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.55
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.98
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.09
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.70
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.23
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.20
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10170.14
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.89
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.35
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.00
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.68
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.85
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11888.45
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.28
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999818849
 
 Normal statistic for number of bits   :   -1.43
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.06
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999978470
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 238                :    0.04
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:01.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35420
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.04
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     641
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    4.45
 p-value of test no 36                 :  5.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     251
 p-value of test no 37                 :    0.9980
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.54
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.70
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.14
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.78
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.00
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.21
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.17
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  508.00
 p-value of test no 55                 :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.00
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.87
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.19
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.21
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.38
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.51
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5188.83
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45889
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869889
   j =  1                              :        399908225
   j =  2                              :            45883
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907959
   j =  2                              :            46010
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
 p-value of test no 80                 :    0.9977
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.019
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.43
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.60
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.54
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.89
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.85
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.08
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.11
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.29
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.14
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.02
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17474.25
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.55
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.59
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.71
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.35
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.48
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.29
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.81
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.13
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.49
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.12
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.58
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.03
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.39
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.71
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.04
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.66
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.21
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.25
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.78
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.65
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.43
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.21
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.34
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.33
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.40
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.47
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.60
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.78
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.82
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 185                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 187                :  9.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 188                :    0.9908
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.98
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.34
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.60
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.65
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.70
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.50
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.071
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.92e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.76
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.12
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.76
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4045.96
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.47
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.42
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.08
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000016426
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.49
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999965309
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.21
 p-value of test no 254                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:22.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35421
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5275
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.48
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.82
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.22
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.02
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.13
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.58
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.32
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.11
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.88
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.88
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.96
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6931.09
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.48
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.86
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.15
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.92
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.82
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908032
   j =  2                              :            45978
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45694
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869694
   j =  1                              :        399908617
   j =  2                              :            45684
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
 p-value of test no 104                :    0.9976
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.63
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.90
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.14
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.32
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.41
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.51
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.68
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.37
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.74
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.90
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.25
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.35
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.89
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.78
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.41
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.06
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.30
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.47
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.07
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.62
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.13
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.51
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.35
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.11
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.92
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.31
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.99
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.10
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.26
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.62
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.61
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.25
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.64
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.98
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.20
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.54
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.98
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.66
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.96
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 188                :  9.2e-3
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-3
 p-value of test no 191                :    0.99
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 195                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.11
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.13
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.62
 p-value of test no 200                :  1.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    6.07
 p-value of test no 202                :  9.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  148.02
 p-value of test no 203                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.94
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.18
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.94
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 218                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.30
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.20
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.99
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.03
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11635.83
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.81
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000027106
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.12
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000006847
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 243                :    0.06
 
 Sample variance                       :    2.14
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:56.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35422
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.87
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 34                 :    0.9966
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.79
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     123
 p-value of test no 43                 :    0.99
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.63
 p-value of test no 48                 :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.40
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.35
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.22
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.93
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.63
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.09
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.26
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.83
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7245.73
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.46
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.06
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.16
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.54
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4921.94
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907845
   j =  2                              :            46076
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907821
   j =  2                              :            46085
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.59
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.20
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.86
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.43
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.96
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.96
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.72
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.18
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.83
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.81
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.29
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.78
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.11
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.32
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.95
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.84
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.96
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.90
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.42
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.23
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.84
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.18
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.68
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.97
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.71
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.79
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.60
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.69
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.21
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.88
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.55
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.59
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  136.88
 p-value of test no 175                :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.073
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 186                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.57
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.42
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.55
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.56
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.62
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5043.44
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.19
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.47
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.23
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.89
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12242.99
 p-value of test no 230                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.25
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999955742
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.64
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000041209
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:27.55
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 C (L=10000, r=15)   0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35423
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 12                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.65
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.92
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.82
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.39
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.67
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.53
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.64
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7108.29
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.87
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.90
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  166.12
 p-value of test no 67                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.11
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45320
 p-value of test no 70                 :    0.9955
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869320
   j =  1                              :        399909362
   j =  2                              :            45316
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45776
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869776
   j =  1                              :        399908454
   j =  2                              :            45764
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.23
 p-value of test no 117                :  6.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.96
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.27
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.43
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.09
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.37
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.69
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.15
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.44
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.96
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.55
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.27
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.44
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.83
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.07
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.61
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.41
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.67
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.63
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.00
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.34
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.62
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.11
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.34
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.67
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.73
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.81
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.24
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.08
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.41
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.04
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.56
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.98
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.33
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.05
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.05
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.59
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.77
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.30
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.97
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.88
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.58
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.16
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.72
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.39
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.73
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.07
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.28
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999988007
 
 Normal statistic for number of bits   :  -0.095
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.94
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000068620
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 253                :    0.46
 
 Sample variance                       :    2.09
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:20.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  57  AppearanceSpacings, r = 0       6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35424
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.77
 p-value of test no 29                 :  3.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    3.47
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     659
 p-value of test no 31                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.64
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.34
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.49
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.92
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.94
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.12
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.74
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.62
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.67
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.71
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.10
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.14
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.56
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.37
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5052.83
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908253
   j =  2                              :            45863
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908575
   j =  2                              :            45708
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 94                 :  1.5e-4    *****
 
 Anderson-Darling statistic = A2       :    4.49
 p-value of test no 95                 :  5.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  4.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.29
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.20
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.91
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.20
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.09
 p-value of test no 123                :    0.9935
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.49
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.30
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.13
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.03
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.95
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.73
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17093.23
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.28
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.94
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.71
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.22
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.89
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.39
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.26
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.85
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.57
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.78
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.71
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.80
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.13
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.45
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.26
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.97
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.74
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.24
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.94
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.32
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.19
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.33
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.31
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.89
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.90
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.04
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.07
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.03
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.39
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.93
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.45
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.27
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.23
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.35
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.68
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4726.07
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4262.47
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.52
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.92
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.75
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.86
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000098167
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.50
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999918116
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 253                :    0.49
 
 Sample variance                       :    3.19
 p-value of test no 254                :  7.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:30.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35425
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 19                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 20                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.83
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9953
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    3.53
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.17
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.61
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.03
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.99
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.48
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.37
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.67
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.48
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.83
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7009.80
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.69
 p-value of test no 58                 :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.90
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.62
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.66
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.84
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.49
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45890
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869890
   j =  1                              :        399908223
   j =  2                              :            45884
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
 p-value of test no 94                 :    0.9968
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 95                 :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9989
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.70
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.07
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.41
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.35
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.34
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.43
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.24
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.94
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.47
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.78
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.97
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.25
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.64
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.40
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.68
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.77
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.81
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.45
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.88
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.72
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.48
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.81
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.10
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.50
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.78
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.46
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.17
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.48
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.90
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.26
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.65
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.24
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.88
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.21
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.30
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.20
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.19
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.66
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.81
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.61
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.90
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.83
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.66
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.64
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.08
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.77
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.14
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.14
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.29
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.86
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.44
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.99
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.03
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999947570
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.82
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999991994
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    2.51
 p-value of test no 249                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.75
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:25.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35426
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5279
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.91
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.96
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.92
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.20
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.51
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.93
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.03
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.30
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.39
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.93
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.74
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.89
 p-value of test no 65                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.65
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.77
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.31
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907874
   j =  2                              :            46057
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45380
 p-value of test no 71                 :    0.9902
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869380
   j =  1                              :        399909243
   j =  2                              :            45374
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.73
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.39
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.15
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.18
 p-value of test no 122                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.38
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.49
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.57
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.62
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.32e-3
 p-value of test no 131                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.26
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.62
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.07
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.54
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17717.90
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.84
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.92
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.32
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.95
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.90
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.91
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.60
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.91
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.16
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.05
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.99
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.96
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.52
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.72
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.33
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.87
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.51
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.65
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.54
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.28
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.52
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.96
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.99
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.52
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.11
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.35
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.54
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.97
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.65
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.98
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.13
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.63
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.40
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
 p-value of test no 205                :    0.9943
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.18
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.20
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.82
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.39
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.55
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.88
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.93
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.48
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.36
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.76
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999984275
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.98
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000023713
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.50
 p-value of test no 248                :    0.93
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.046
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.55
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35427
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 12                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 19                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    4.16
 p-value of test no 24                 :  7.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     847
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.57
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.06
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.66
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.93
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.29
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.04
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.72
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.53
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.97
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7013.63
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.67
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.72
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.32
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.01
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4909.88
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908254
   j =  2                              :            45870
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 101                :    0.9937
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 118                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.25
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.03
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.20
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.99
 p-value of test no 123                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.90
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.20
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.71
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.93
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.89
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 143                :    0.9926
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17054.59
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.41
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.86
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.80
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.85
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.94
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.80
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.01
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.62
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.74
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.85
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.22
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.71
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.86
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.48
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.97
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.62
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.75
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.61
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.19
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.73
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.29
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.26
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.12
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.19
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.63
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.09
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.64
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 195                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.84
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.54
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.01
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.42
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.41
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.71
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
 p-value of test no 220                :    0.9914
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4735.14
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.06
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.09
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.36
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12108.04
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.90
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.94
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999936701
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.35
 p-value of test no 233                :  7.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000023644
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:04.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35428
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.56
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.67
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 34                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    4.63
 p-value of test no 36                 :  4.3e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.90
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.34
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.63
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.57
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.74
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.78
 p-value of test no 51                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.13
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.03
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.86
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.09
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7302.55
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.71
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.10
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.77
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.62
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908744
   j =  2                              :            45625
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45386
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869386
   j =  1                              :        399909231
   j =  2                              :            45380
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.22e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.67
 p-value of test no 115                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.98
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.85
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.46
 p-value of test no 121                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.85
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.10
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.77
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.77
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.53
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.95
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.11
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17643.33
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.02
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.99
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.18
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.31
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.25
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.14
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.34
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.13
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.70
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.89
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.23
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.78
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.51
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.39
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.63
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.80
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.15
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.54
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.82
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.13
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.27
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.77
 p-value of test no 169                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.13
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.28
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.89
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.07
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.25
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.99
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.08e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.22
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.71
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.29
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 208                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9646.18
 p-value of test no 211                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 212                :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.27
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.86
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.43
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.82
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.39
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.63
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.48
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.79
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999995555
 
 Normal statistic for number of bits   :  -0.035
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.74
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000139900
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:35.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35429
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5168
 p-value of test no 13                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7071
 p-value of test no 15                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.43
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.18
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.18
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.68
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.57
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.37
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.32
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.67
 p-value of test no 56                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.82
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.99
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.59
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.78
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.38
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908008
   j =  2                              :            45990
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908300
   j =  2                              :            45844
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 77                 :    0.9949
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.015
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.01
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.70
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.52
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.71
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.13
 p-value of test no 124                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.08
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.46
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.48
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.00
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17358.11
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.95
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.77
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.05
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.00
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.14
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.76
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   14.24
 p-value of test no 152                :    0.9993    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.67
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.16
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.90
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.78
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.11
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.83
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.93
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.56
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  179.14
 p-value of test no 164                :  7.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.85
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.69
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.60
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.31
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.43
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.11
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.74
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.52
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.62
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.75
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.40
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.94
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.24
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 206                :  6.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.88
 p-value of test no 207                :    0.9961
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.92
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.20
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.88
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.14
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.50
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.83
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12121.04
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.54
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.34
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000009745
 
 Normal statistic for number of bits   :   0.077
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.18
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000003124
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:35.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         0.9997 
  75  RandomWalk1 M (L=50, r=25)      0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35430
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 7                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 11                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 12                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 41                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.05
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.95
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.45
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.89
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.03
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.43
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.28
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.28
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.93
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.86
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.22
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.54
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46176
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907651
   j =  2                              :            46170
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908361
   j =  2                              :            45815
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.32
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.99
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.98
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.83
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.86
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.24
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.55
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.94
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17398.83
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.14
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.47
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.61
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.87
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   15.65
 p-value of test no 151                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.43
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.53
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.38
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.49
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.09
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.42
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.76
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.63
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.51
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.03
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.54
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.96
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.12
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.02
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.48
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.39
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.97
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.81
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.55
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.93
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.47
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.79
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.22
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.39
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.84
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.46
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.13
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.68
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9908.78
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.14
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.32
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.67
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.44
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.17
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12055.36
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.16
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999883013
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.02
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999931103
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:53.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35431
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 7                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 9                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 12                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    3.69
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.26
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.63
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.12
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.23
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.08
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.07
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.18
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.67
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.94
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.50
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.71
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5137.21
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908726
   j =  2                              :            45628
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908168
   j =  2                              :            45910
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.98
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.74
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.80
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.49
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 127                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.05
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.33
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.85
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17439.15
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.20
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.62
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   41.26
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.18
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.23
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.82
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.24
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.18
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.92
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.18
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.45
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.33
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.43
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.44
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.00
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.72
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.82
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.96
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.72
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.93
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.01
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.58
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.55
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.47
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.20
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.79
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.47
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.27
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.77
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.05
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.80
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.52
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  155.95
 p-value of test no 203                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.23
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.26
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.79
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.61
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.86
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.00
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.35
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11558.94
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.83
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.12
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999918521
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.13
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000070165
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    2.14
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:07.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35432
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    2.58
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.63
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.25
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.97
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.55
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.32
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.32
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.30
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.70
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.97
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.89
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.90
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.78
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.56
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5119.23
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46165
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907675
   j =  2                              :            46155
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907881
   j =  2                              :            46046
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.47
 p-value of test no 118                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.17
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.00
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.22
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.26
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.49
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.00
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.94
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.72
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.67
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.02
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.74
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.24
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.36
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.08
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.39
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.91
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.22
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.14
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.82
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.26
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.38
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.19
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.54
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.90
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.80
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.36
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.38
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.26
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.62
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.41
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.21
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.31
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.97
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.43
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.50
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.26
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.63
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.60
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.07
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.20
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.19
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 221                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4673.99
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.21
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.41
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.33
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11617.80
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.16
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.07
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999967226
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.23
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999920315
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.16
 p-value of test no 249                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:00.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35433
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.14
 p-value of test no 23                 :  2.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    4.50
 p-value of test no 30                 :  5.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     544
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.27
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.38
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.40
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.57
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.70
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.81
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.88
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.25
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.88
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6786.22
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.50
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.65
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.41
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.93
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.16
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908235
   j =  2                              :            45881
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908399
   j =  2                              :            45799
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 101                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -8.31e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.51
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.13
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.18
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.01
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.42
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.18
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.83
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.96
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.66
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17273.33
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.88
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.94
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.81
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.78
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.95
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.75
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.11
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.31
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.03
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.83
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.86
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.76
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.36
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.31
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.96
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.05
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.50
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.29
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.40
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.47
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.98
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.59
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.22
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.59
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.54
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.42
 p-value of test no 175                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.22
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.034
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.19
 p-value of test no 178                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.10
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.82
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.78
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.48
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.95
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.59
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.72
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.01
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.92
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4309.61
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11646.18
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.04
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.73
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000020890
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.29
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000184594
 
 Normal statistic for number of bits   :    1.46
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.26
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35434
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.24
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.62
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.05
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.27
 p-value of test no 50                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.24
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.12
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.58
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.23
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.07
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7077.27
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.18
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.00
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.37
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.79
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.14
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45819
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869819
   j =  1                              :        399908363
   j =  2                              :            45817
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45456
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869456
   j =  1                              :        399909091
   j =  2                              :            45450
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.00
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.65
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.02
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.47
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.16
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.27
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.77
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.06
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.98
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.08
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.21
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17577.78
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.95
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.88
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.83
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.81
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.51
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.42
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.86
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.06
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.99
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.47
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.73
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.11
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.58
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.40
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.77
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.88
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.87
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.47
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5243.43
 p-value of test no 168                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.95
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.28
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.66
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.21
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.32
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.29
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.22
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.85
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.03
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 180                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.95
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.66
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.14
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10245.69
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.95
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.72
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.33
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3970.79
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.71
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.33
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.43
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.32
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000048901
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.87
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000079195
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:16.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35435
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1467
 p-value of test no 11                 :  3.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334587
   j =  1                              :        599997066
   j =  2                              :             1467
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    4.36
 p-value of test no 27                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 28                 :    0.9987
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 30                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.66
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.70
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.13
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.08
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.33
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.29
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.15
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.84
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.89
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.83
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.98
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908963
   j =  2                              :            45511
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908397
   j =  2                              :            45794
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 72                 :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 76                 :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 77                 :  2.1e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 78                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9906
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-3
 p-value of test no 100                :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.07
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.19
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  103.80
 p-value of test no 121                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.33
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.89
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.69
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.68
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.51
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.69
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.25
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17645.05
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.33
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.03
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.84
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.33
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.01
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.09
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.18
 p-value of test no 155                :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.49
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.45
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.22
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.04
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.21
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.27
 p-value of test no 161                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.98
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.64
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.12
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.72
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.44
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.59
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.87
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.93
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.86
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.61
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.55
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.44
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.58
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.71
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.49
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    2.05
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.70
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.04
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.20
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 210                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.15
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.34
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4789.14
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.93
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.54
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3957.38
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.40
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.78
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.15
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000039322
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.19
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999994418
 
 Normal statistic for number of bits   :  -0.044
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.92
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:00.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 C (L=50, r=25)      0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35436
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5413
 p-value of test no 13                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.97
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.30
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.01
 p-value of test no 51                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.51
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.31
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.26
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.82
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6942.17
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.04
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.82
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.42
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.33
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908257
   j =  2                              :            45861
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908358
   j =  2                              :            45818
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.64
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.77
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.72
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.79
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.94
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.38
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.91
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.04
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.50
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17384.94
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.18
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.08
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.06
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.96
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.38
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.03
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.44
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.39
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.67
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.08
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.06
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.75
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.61
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.42
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.21
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.54
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.67
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.12
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.31
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.64
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.77
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.95
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.65
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.50
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.37
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.17
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.23
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.05
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.62
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.33
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.80
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.40
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.16
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.69
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.08
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.39
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.47
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.81
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12170.61
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.91
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.44
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000078259
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.20
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000113200
 
 Normal statistic for number of bits   :    0.89
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 241                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.61
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:22.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35437
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7125
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.09
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.71
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.99
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.01
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.93
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.71
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.72
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  188.38
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.71
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.51
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7054.15
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.17
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.11
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.13
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.52
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46126
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870126
   j =  1                              :        399907751
   j =  2                              :            46120
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908735
   j =  2                              :            45628
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.80
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.21
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.12
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.06
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.53
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.31
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.86
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.15
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.26
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.14
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.10
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.35
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.87
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.15
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.60
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.56
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.06
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.85
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.47
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.47
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.72
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.03
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.00
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.00
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.99
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.38
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.48
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.00
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.20
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.82
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.93
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5216.86
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.64
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.12
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.02
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.26
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5194.69
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.73
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.86
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.60
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.62
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.22
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.26
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9855.97
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.10
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9960
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.20
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.20
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.17
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.18
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11497.09
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.18
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999843908
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.39
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000003304
 
 Normal statistic for number of bits   :   0.026
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.66
 p-value of test no 236                :  5.0e-5    *****
 
 Anderson-Darling statistic = A2       :    6.32
 p-value of test no 237                :  7.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.96
 p-value of test no 238                :  1.5e-3
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 243                :    0.81
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35438
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 11                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5419
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 18                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.29
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.39
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.06
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.05
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.20
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.68
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.40
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.32
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6943.43
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.61
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.48
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.49
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.88
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.83
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908447
   j =  2                              :            45772
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45488
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869488
   j =  1                              :        399909025
   j =  2                              :            45486
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.83e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.31
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.44
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.28
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.66
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.97
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.83
 p-value of test no 125                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.38
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.40
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.88
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.85
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.89
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.41
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.73
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.29
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.64
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.83
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.62
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.28
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.30
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.83
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.45
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.99
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.51
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.22
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.62
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.23
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.52
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.06
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.10
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.65
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.81
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.78
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.70
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.25
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.60
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.93
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.58
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.67
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.00
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.86
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.44
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.54
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.27
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.76
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.48
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.26
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.91
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -4.25
 p-value of test no 217                : 1 -  1.1e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.83
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.10
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.36
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.58
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.61
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11535.38
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.23
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000039730
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.34
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999876689
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.64
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:16.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300           1 -  1.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35439
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5295
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7148
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.72
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.83
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.35
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.79
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.39
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.70
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.09
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1370.51
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.70
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.26
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.85
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.85
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.62
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.29
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908385
   j =  2                              :            45800
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907849
   j =  2                              :            46071
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.07
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.17
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.97
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.52
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.38
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.02
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.031
 p-value of test no 134                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.32
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.48
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17427.22
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.05
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.08
 p-value of test no 147                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.53
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.28
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.85
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.36
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.54
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.27
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.28
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.35
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.89
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.56
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.18
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.01
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.58
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.58
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.18
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.22
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.41
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.01
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.75
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.80
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.76
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.36
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.31
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.93
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  473.31
 p-value of test no 174                :  6.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.43
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.44
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.48
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.27
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9766.99
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.55
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.37
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.02
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.17
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.86
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.90
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.97
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.57
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000128359
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.14
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000053860
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 R (L=10000, r=15)   6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35440
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 3                  :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.35
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.02
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.46
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.73
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.94
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.93
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.00
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.10
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.25
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.98
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.85
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.15
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.54
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.89
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.43
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45865
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869865
   j =  1                              :        399908273
   j =  2                              :            45859
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45535
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869535
   j =  1                              :        399908932
   j =  2                              :            45531
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.57e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 116                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.09
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.60
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.27
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.13
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.65
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.76
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.14
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.11
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.13
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.06
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17574.67
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.88
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.79
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.41
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.35
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.33
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.25
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.61
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.18
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.80
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.27
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.62
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.53
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.78
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.61
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.82
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.47
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.82
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.29
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.97
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.83
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.89
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.00
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.12
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.04
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.14
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.34
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.75
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.78
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.63
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 185                :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-4
 p-value of test no 191                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.86
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.90
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.19
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.22
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 214                :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.01
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.55
 p-value of test no 222                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.01
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.79
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.76
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.84
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12167.05
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.21
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000063460
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.42
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999974360
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:35.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35441
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5445
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.25
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.70
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.86
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.40
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.62
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.39
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.11
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.61
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1489.36
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7290.42
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.07
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.37
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.31
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.33
 p-value of test no 67                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.09
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45613
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869613
   j =  1                              :        399908777
   j =  2                              :            45607
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.056
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.92
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.70
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.27
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.81
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.98
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.37
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.78
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.34
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.81
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.22
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.53
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.32
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.96
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.29
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.09
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.56
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.20
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.28
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.62
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.78
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.84
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.80
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.62
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.79
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.62
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.81
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.16
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.10
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.60
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.29
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.93
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.75
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.43
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.03
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  237.12
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.12
 p-value of test no 176                :  5.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.75
 p-value of test no 177                :    0.9970
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.46
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.26
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.17
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.62
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.85
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 208                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9729.64
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.81
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5019.02
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.72
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.67
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.22
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12235.64
 p-value of test no 229                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.61
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.23
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999981209
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.43
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999920027
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:26.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35442
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.14
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.82
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.88
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.09
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.06
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.47
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.04
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.70
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.14
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.29
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.93
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6792.66
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.97
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.23
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.63
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.50
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908422
   j =  2                              :            45780
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907833
   j =  2                              :            46076
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 90                 :  6.3e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    5.78
 p-value of test no 92                 :  1.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.028
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.22
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.48
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.47
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.74
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.37
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.54
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.46
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17295.95
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.91
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.60
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.29
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.04
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.38
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.25
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.37
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.72
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.48
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.27
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.82
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.93
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.30
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.38
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.59
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.99
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.84
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.24
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.57
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.23
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.65
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.53
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.27
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.71
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.78
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.30
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.07
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 186                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    3.52
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.43
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.01
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.92
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.64
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.85
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.42
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.57
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.32
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.75
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.14
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.24
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.08
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999969440
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.70
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000132124
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.031
 p-value of test no 238                :    0.49
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 253                :    0.9923
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:19.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35443
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 7                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.50
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.17
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.15
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.19
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.20
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.42
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  380.58
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.27
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.52
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.99
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.34
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.98
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.01
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.06
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45929
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869929
   j =  1                              :        399908146
   j =  2                              :            45921
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46098
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870098
   j =  1                              :        399907810
   j =  2                              :            46086
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.064
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.62
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.40
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.63
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.72
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.24
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.68
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.23
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 127                :  5.2e-4    *****
 
 Anderson-Darling statistic = A2       :    4.88
 p-value of test no 128                :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.96
 p-value of test no 129                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.52
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.73
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17559.48
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.81
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.58
 p-value of test no 147                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.16
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.99
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.17
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.13
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.92
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.45
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.10
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.65
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.87
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.66
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.71
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.86
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.86
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.01
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.00
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.09
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.72
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  299.52
 p-value of test no 166                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.64
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5160.37
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.05
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.71
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.43
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.43
 p-value of test no 172                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.90
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.06
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.62
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.94
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.14
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.66
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.29
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.28
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.30
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.22
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10284.86
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.19
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.39
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.77
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.76
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.67
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11447.45
 p-value of test no 230                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.20
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000079003
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.55
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000061708
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 248                :    0.32
 
 Sample variance                       :    2.19
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:46.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)    0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35444
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     966
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    4.19
 p-value of test no 26                 :  7.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.31
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.94
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.35
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.18
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.21
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.15
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.30
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.10
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.93
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6826.98
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.55
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.25
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.54
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.85
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.04
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908174
   j =  2                              :            45913
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908610
   j =  2                              :            45692
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 118                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.34
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.66
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.00
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.28
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.92
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.51
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.22
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.85
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.67
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.82
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.10
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.70
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.28
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.79
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.29
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.14
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.96
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.62
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.90
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.16
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.68
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.09
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.06
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.88
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.14
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.13
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.67
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   49.02
 p-value of test no 165                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.35
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.53
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.87
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.15
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.53
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.35
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.41
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.51
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.54
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.70
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.58
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.36
 p-value of test no 179                :  3.9e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.70
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.10
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.49
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.98
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.78
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.86
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.76
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.62
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4295.01
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.32
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.59
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.29
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.16
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000085546
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.28
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999966347
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 253                :    0.06
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  81  LinearComp, r = 29              3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35445
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1492
 p-value of test no 12                 :  3.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334612
   j =  1                              :        599997016
   j =  2                              :             1492
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 44                 :    0.9945
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.06
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.41
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.47
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.50
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.06
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.05
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.75
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.30
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7218.92
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.24
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.97
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.14
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.14
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908447
   j =  2                              :            45772
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908467
   j =  2                              :            45762
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 74                 :    0.9982
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.50
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.20
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.29
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.94
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.01
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.38
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.33
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 132                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.51
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.93
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.82
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17280.97
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.27
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.06
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.66
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.49
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.19
 p-value of test no 150                :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.52
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.09
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.00
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.44
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.11
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.59
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.53
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.00
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.42
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.59
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.79
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.58
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.62
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.26
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5156.88
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.88
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.11
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.39
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.04
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.63
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.91
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.93
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.52
 p-value of test no 178                :    0.9906
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.64
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.52
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.76
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.79
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.83
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 219                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4637.41
 p-value of test no 222                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.26
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.73
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4295.42
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.36
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.02
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.62
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999923078
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999861449
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:31.64
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35446
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 8                  :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.27
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.04
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.93
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.00
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.06
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.71
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.35
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1359.71
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.29
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.05
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.10
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.83
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.44
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.69
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908415
   j =  2                              :            45788
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908730
   j =  2                              :            45629
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.040
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.26
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.88
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.76
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.13
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.27
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.34
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.40
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.22
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.14
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.30
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17658.99
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.01
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.97
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.57
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.75
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.07
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.90
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.22
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.85
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.96
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.48
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.07
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.44
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.65
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.86
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.57
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.71
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.61
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.02
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.08
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.58
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.23
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.10
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  258.01
 p-value of test no 170                :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.21
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.19
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.05
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.72
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.14
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.76
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.27
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.70
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.20
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.86
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.31
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.80
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.79
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.63
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.70
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.58
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11634.47
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.64
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.41
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999939938
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.28
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999962573
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.78
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:06.10
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   8  CollisionOver, t = 7            7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35447
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 8                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 11                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 12                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    3.94
 p-value of test no 39                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.04
 p-value of test no 41                 :  9.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.46
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.37
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   39.94
 p-value of test no 49                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.98
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.96
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.54
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.74
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7157.04
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.79
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.37
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.47
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4938.22
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908439
   j =  2                              :            45779
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908363
   j =  2                              :            45811
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.15
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.68
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.14
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.92
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.89
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.57
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.55
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.91
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.20
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.57
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.97
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.67
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.04
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.91
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.87
 p-value of test no 151                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.36
 p-value of test no 152                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.30
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.68
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.13
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.03
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.47
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.77
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.65
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.31
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.68
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.12
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.15
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.63
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.28
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.01
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.26
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.20
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.01
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.45
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.08
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.53
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.04
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.10
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.92
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.48
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 188                :    0.13
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.18
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.97
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  253.12
 p-value of test no 207                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.17
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10156.35
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.92
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.48
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.71
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.54
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11596.16
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11597.25
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.91
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999973898
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.54
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999969638
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    2.03
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 248                :    0.68
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:32.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35448
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997193
   j =  2                              :             1402
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 7                  :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    3.55
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.59
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    4.02
 p-value of test no 45                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.08
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.46
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.19
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.54
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.42
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.40
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.46
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1522.07
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.70
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.40
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.83
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.12
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.81
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908257
   j =  2                              :            45867
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.01
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.88
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.58
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.38
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.39
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.61
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.70
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.68
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17284.30
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.80
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.04
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.70
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.13
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.27
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.03
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.00
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.38
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.31
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.04
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.10
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.87
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.57
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.36
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.40
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.18
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.71
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.13
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.97
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.70
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.81
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.83
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.19
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.22
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.70
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.31
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.79
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.67
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.14
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.51
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.70
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.02
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9851.66
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.56
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.38
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.25
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.10
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.25
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.91
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.59
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.90
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999872864
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.38
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999961787
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.97
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-3
 p-value of test no 250                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:36.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35449
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    3.61
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 27                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.9906
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    4.01
 p-value of test no 45                 :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.90
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.33
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.28
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.01
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.12
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.03
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.31
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.38
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.05
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.92
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.36
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.58
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.85
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4813.66
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908372
   j =  2                              :            45814
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908505
   j =  2                              :            45740
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
 p-value of test no 86                 :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 87                 :  2.2e-3
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 88                 :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.78
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.61
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.40
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.68
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.51
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.36
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.39
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.83
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.66
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.22
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17852.90
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.11
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.30
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.17
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.32
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.97
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.96
 p-value of test no 151                :    0.9948
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.20
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.27
 p-value of test no 154                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.88
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.39
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.32
 p-value of test no 158                :    0.9918
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.99
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.30
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.48
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.83
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.93
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.29
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.03
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.59
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.58
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.86
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.40
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.45
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.68
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.74
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.15
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.40
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.52
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.69
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.59
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.57
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.89
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.31
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.62
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.93
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.00
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.77
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.23
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.01
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.75
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.67
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.71
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12116.31
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11987.89
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.10
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999894365
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.15
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000188902
 
 Normal statistic for number of bits   :    1.49
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    2.81
 p-value of test no 239                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:20.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35450
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 10                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5337
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 21                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.31
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.04
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.54
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.73
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.49
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.20
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  392.19
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.37
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.52
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.63
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.59
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.62
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.62
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.08
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908575
   j =  2                              :            45705
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 85                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 94                 :    0.9930
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.94
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.99
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.39
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.79
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.07
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.48
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.68
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.62
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 131                :    0.9931
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.64
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.36
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.99
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.54
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.39
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.56
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.54
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.97
 p-value of test no 151                :    0.9912
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.68
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.50
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.55
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.24
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.72
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.91
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.16
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.11
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.46
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.92
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.61
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.45
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.65
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.64
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.56
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.74
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.20
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.06
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.71
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.36
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.06
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.83
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.06
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.35
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.028
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.33
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.79
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.68
 p-value of test no 198                :  8.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.55
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.49
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 208                :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10245.96
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.90
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.69e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.37
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.38
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4100.35
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.61
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12192.51
 p-value of test no 229                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.85
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.15
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000064033
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.35
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999928556
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:06.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  47  MaxOft AD, t = 16               0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35451
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1493
 p-value of test no 10                 :  3.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334613
   j =  1                              :        599997014
   j =  2                              :             1493
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4210
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.11
 p-value of test no 34                 :  9.3e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    3.05
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.50
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.82
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.14
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.75
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.81
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.90
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.95
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.69
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.63
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.10
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.63
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.20
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.58
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.89
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.00
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.83
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.15
 p-value of test no 67                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.01
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45688
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869688
   j =  1                              :        399908627
   j =  2                              :            45682
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908673
   j =  2                              :            45659
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.87
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.08
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.38
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.84
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.24
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.86
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.48
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.84
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 130                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.65
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.05
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 143                :    0.9936
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17109.70
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.06
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.03
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.28
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.64
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.57
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.71
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.11
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.83
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  195.62
 p-value of test no 159                :  6.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.02
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.97
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  557.29
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.09
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.90
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.32
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.96
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.89
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.17
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.78
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.75
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.49
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.10
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.97
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.98
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.80
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.49
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.78
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.96
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.82
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.52
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.93
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.16e-3
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.25
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.99
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.21
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.93
 p-value of test no 228                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.15
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.46
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.51
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000036553
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.23
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000017983
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
 p-value of test no 241                :    0.9913
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:25.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           3.1e-4
  24  ClosePairs NP, t = 9            9.3e-4
  76  RandomWalk1 R (L=1000, r=0)     6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35452
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.19
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.51
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.87
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.20
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.58
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.83
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.88
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  296.22
 p-value of test no 54                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.17
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.52
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7006.46
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.19
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.92
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.29
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.12
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.54
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907657
   j =  2                              :            46170
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908537
   j =  2                              :            45727
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 102                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.81e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -4.47e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.74
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.60
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.01
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.87
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.81
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.32
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.32
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.69
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.47
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.48
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.48
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17317.37
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.32
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.73
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.43
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.99
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.27
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.73
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.99
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.10
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.82
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.98
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.56
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.59
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.14
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.50
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.26
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.68
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.65
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.67
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.06
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.12
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.87
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.83
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.48
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.31
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.79
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4770.03
 p-value of test no 173                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.53
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.59
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.21
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.34
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.97
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.70
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.18
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.98
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.25
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.78
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.28
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.09
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.65
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.81
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.16
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000007261
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.75
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999985895
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 248                :    0.73
 
 Sample variance                       :    1.56
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:01.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35453
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5572
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7085
 p-value of test no 19                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.01
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.19
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.09
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.02
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.10
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.28
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.65
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.15
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.78
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7141.66
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.39
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.84
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.37
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.37
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.79
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45598
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869598
   j =  1                              :        399908810
   j =  2                              :            45586
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46071
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870071
   j =  1                              :        399907863
   j =  2                              :            46061
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.87
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.43
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.86
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.40
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.38
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.54
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.68
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.05
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.84
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.84
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.11
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.31
 p-value of test no 136                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.32
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.99
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17138.56
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.15
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.52
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.38
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.81
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.54
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.02
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.91
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.61
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.45
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.98
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.90
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.32
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.71
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.57
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.43
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.00
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.96
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.57
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.45
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.21
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.40
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.11
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.83
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.91
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.24
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4837.66
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.08
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.00
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.93
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.44
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.32
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.90
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.00
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.54
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.22
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.87
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.63
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.08
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.53
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.40
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11460.70
 p-value of test no 230                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.08
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999932888
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.90
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999990161
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.10e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35454
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997337
   j =  2                              :             1330
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4451
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     177
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.73
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.46
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.87
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.61
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.47
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.23
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.72
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.55
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.06
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.47
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.37
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   38.14
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.23
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.47
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4828.82
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46274
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870274
   j =  1                              :        399907454
   j =  2                              :            46270
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45675
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869675
   j =  1                              :        399908656
   j =  2                              :            45663
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-5
 p-value of test no 113                :    0.9940
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.19
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.93
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.05
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.05
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.21
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.81
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.13
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.43
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.08
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.44
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.82
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.28
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.73
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.80
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.59
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.00
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.24
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.55
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.04
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.98
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.47
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.33
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.06
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.20
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.17
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.91
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.96
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.63
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.13
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.61
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.53
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.38
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.62
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.25
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.35
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.20
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.83
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.31
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.91
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.30
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.84
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.51
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.22
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.39
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.50
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.63
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.16
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.43
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.71
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4757.99
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.27
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.72
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.32
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.27
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.94
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.53
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000000796
 
 Normal statistic for number of bits   : 6.29e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.72
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999965570
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:50.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35455
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    3.91
 p-value of test no 26                 :  9.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.83
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.36
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.76
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.02
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.37
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.14
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.37
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.64
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.73
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.32
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.31
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.57
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.66
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.04
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46354
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870354
   j =  1                              :        399907298
   j =  2                              :            46342
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908835
   j =  2                              :            45578
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 93                 :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  7.7e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.021
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.52
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.23
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.95
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.19
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.17
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.37
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.77
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.10
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.57
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.25
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.68
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.33
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.99
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.52
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.13
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.05
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.81
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.17
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.54
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.02
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.68
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.79
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.62
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.29
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.70
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.51
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.47
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.38
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.97
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.06
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.37
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.69
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.57
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.64
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.52
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.73
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.49
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.24
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.93
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.28
 p-value of test no 176                :    0.9932
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.051
 p-value of test no 177                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.59
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.46
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.16
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.28
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.16
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9712.91
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.25
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.41
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.43
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.28
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.53
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.79
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.09
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999952898
 
 Normal statistic for number of bits   :   -0.37
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.05
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000040180
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 235                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:50.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35456
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 20                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    2.71
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.79
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.69
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.35
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.71
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.53
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.39
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7246.85
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.86
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.43
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.50
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.52
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.23
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45978
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869978
   j =  1                              :        399908048
   j =  2                              :            45970
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46164
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907676
   j =  2                              :            46156
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.15
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.43
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.42
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.16
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.19
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.87
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.12
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.01
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.08
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17433.82
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.38
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.76
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.15
 p-value of test no 148                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.62
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.81
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.03
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.47
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.52
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.68
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.76
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.90
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.70
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.38
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.62
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.51
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.20
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.61
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.68
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.23
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.83
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.58
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.34
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.85
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.38
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.31
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5153.49
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.69
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.62
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.71
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.49
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.03
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.02
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9753.90
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.00
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.043
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 220                :    0.9952
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4721.43
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 224                :    0.9934
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.18
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.45
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.41
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.57
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11557.72
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.65
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000061414
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.40
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000007720
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35457
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1254
 p-value of test no 11                 :    0.9987
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334374
   j =  1                              :        599997492
   j =  2                              :             1254
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 12                 :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5529
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.51
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.81
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.32
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.61
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.39
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.03
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.57
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.67
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.61
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.92
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.43
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.11
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.79
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908137
   j =  2                              :            45927
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45964
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869964
   j =  1                              :        399908075
   j =  2                              :            45958
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.45
 p-value of test no 115                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.63
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.42
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.26
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.09
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.41
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.34
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.75
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.94
 p-value of test no 129                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.33
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17522.72
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.82
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.29
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.89
 p-value of test no 148                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.31
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.94
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.90
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.21
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.12
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.38
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.95
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.44
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.28
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.04
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.73
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.05
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.05
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.96
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.11
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.55
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.81
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.55
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.81
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  141.15
 p-value of test no 170                :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.62
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.14
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.72
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.15
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.10
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.50
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.62
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.75
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.22
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.47
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.15
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.91
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.46
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4997.09
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.35
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.86
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.64
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12056.29
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.06
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  8000024418
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.66
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000007219
 
 Normal statistic for number of bits   :   0.057
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.093
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:08.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 C (L=10000, r=0)    0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35458
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.60
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.11
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.57
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.32
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.20
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.89
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.63
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7200.38
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.43
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.86
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.38
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.92
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.45
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908256
   j =  2                              :            45863
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908205
   j =  2                              :            45896
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 86                 :  1.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.07
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.88
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.17
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.71
 p-value of test no 124                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.22
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
 p-value of test no 127                :    0.9978
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.03
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.19
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.14
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17194.23
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.43
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.37
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.57
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.48
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.71
 p-value of test no 152                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.23
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.97
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.74
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.48
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.61
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.59
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.46
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.72
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.09
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.20
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   46.40
 p-value of test no 165                :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.98
 p-value of test no 166                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.65
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.10
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.91
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.93
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.40
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.02
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5072.25
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.57
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.29
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.78
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 182                :    0.9907
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.28
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.37
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.17
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.07
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.45
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.100
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.07
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4992.37
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.87
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.21
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.83
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12117.08
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.96
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000057442
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.43
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000097411
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.30
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:40.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35459
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 12                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 22                 :    0.9960
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 23                 :    0.9927
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.16
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.65
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.34
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.96
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.24
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.48
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.13
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.75
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.44
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1310.23
 p-value of test no 56                 :    0.9924
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.03
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.86
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.04
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.41
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.98
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.66
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907805
   j =  2                              :            46090
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908535
   j =  2                              :            45728
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.62
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.67
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.87
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.96
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.34
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.95
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.76
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.06
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.011
 p-value of test no 135                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.50
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.49
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17230.33
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.60
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.10
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   37.46
 p-value of test no 150                :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.92
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.88
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.95
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.36
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.16
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.24
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.14
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.56
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.82
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.58
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.71
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.61
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.35
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.62
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.90
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.57
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.33
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.30
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.34
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.60
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.08
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.62
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.97
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.80
 p-value of test no 175                :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.05
 p-value of test no 176                :    0.9952
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.97
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 183                :    0.21
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.26
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.80
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.52
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.06
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10215.75
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.73
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.13
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.61
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.26
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.30
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12154.37
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.67
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999894188
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.73
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999895457
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 241                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 242                :  4.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 243                :  7.9e-3
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 248                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  69  MatrixRank, L=1000, r=26        0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35460
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.60
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.14
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.04
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.14
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.08
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.16
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.65
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.44
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.11
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.24
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7139.59
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.26
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.56
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.86
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.98
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907891
   j =  2                              :            46050
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907936
   j =  2                              :            46023
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.12
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.61
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.62
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.36
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.50
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.18
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.97
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.20
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17371.44
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.70
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.86
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.98
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.55
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.26
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.20
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.20
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.55
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.12
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.56
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.89
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.60
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.35
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.59
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.46
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.44
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.10
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.28
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.57
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.33
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.48
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.28
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.89
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.38
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.16
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.13
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.14
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 179                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.45
 p-value of test no 198                :    0.9935
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.14
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.88
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10013.79
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10138.66
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.84
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.35
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.31
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.27
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.59
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.19
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.74
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999957533
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.08
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999928727
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.10
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.87
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:02.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35461
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.13
 p-value of test no 23                 :  2.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.69
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.60
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.46
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.34
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.83
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  280.89
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.87
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.21
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.65
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-3
 p-value of test no 58                 :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.66
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.15
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.86
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.82
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908359
   j =  2                              :            45819
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907881
   j =  2                              :            46052
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-3
 p-value of test no 86                 :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.9932
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  117.03
 p-value of test no 119                :  1.5e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.17
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.25
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.01
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.64
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.01
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.87
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.35
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.12
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.09
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17208.59
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.35
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.32
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.49
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.20
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.28
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.37
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.24
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.82
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.89
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.43
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.59
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.84
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.96
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.44
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.35
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.14
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.84
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.99
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.43
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.69
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.41
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.30
 p-value of test no 168                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.09
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.82
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.86
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.88
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.58
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.43
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.82
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.01
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.75
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.48
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.70
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.35
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.67
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.23
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.88
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.06
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.10
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.88
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4259.71
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.92
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.47
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.13
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000007957
 
 Normal statistic for number of bits   :   0.063
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.04
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999907517
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 251                :    0.05
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.30
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.40
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:45.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  59  WeightDistrib, r = 0            1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35462
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4150
 p-value of test no 14                 :    0.9978
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    3.48
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.42
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.75
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.54
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.15
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :  113.52
 p-value of test no 52                 :  4.0e-6    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.22
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.23
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.64
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.85
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.47
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 60                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.98
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.42
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   87.41
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.49
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46162
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870162
   j =  1                              :        399907681
   j =  2                              :            46152
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.67
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.71
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.36
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.37
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.67
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.70
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.96
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.44
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.31
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.40
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17245.04
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.21
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.23
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.92
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.45
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.90
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.21
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.31
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.87
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.88
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.73
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.73
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.16
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.72
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.14
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.48
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.68
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.73
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.19
 p-value of test no 165                :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.12
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.81
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.92
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.14
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.44
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.70
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.84
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.09
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.15
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.46
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.01
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.90
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.45
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.74
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.52
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.040
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.29
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.82
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.15
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.15
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.35
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11588.62
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.97
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000094420
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.12
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000022927
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.15
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:21.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         4.0e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35463
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 11                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7503
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.69
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.36
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.07
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.63
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.09
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.44
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.44
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.38
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.83
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.66
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.56
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.36
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908076
   j =  2                              :            45959
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908032
   j =  2                              :            45975
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.31
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.87
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.79
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.15
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.87
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.10
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.63
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.74
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.20
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.80
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17202.40
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.34
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.88
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.82
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.42
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.00
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.79
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.78
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.16
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.44
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.20
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.35
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.13
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.36
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.87
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.20
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.14
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.85
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.60
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.39
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.26
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.63
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.72
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.40
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.33
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.38
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.63
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.73
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.46
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.34
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10267.79
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.15
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.98
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5092.03
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.44
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.12
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11700.35
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11621.70
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.80
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000128638
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.51
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000020257
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35464
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 38                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.84
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.54
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.17
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.81
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.82
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.48
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.18
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.57
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.97
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.17
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.91
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.50
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.03
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45614
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869614
   j =  1                              :        399908777
   j =  2                              :            45604
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908301
   j =  2                              :            45842
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.16
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.46
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.68
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.96
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.43
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.42
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.74
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17029.70
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.37
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.08
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.17
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.11
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.17
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.78
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.26
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.66
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.29
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.88
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.70
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.57
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.28
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.27
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.99
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.48
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.15
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.46
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.22
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.38
 p-value of test no 167                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.75
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.39
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  255.60
 p-value of test no 170                :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.34
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.00
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.77
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  316.93
 p-value of test no 174                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.08
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.82
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    2.54
 p-value of test no 189                :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.50
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.48
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.83
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.63
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10106.01
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.20
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.68
 p-value of test no 218                :  3.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5073.67
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.79
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.16
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.37
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11973.70
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.32
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.29
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000044695
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.13
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999865970
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:56.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35465
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5308
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4495
 p-value of test no 17                 :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.81
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    4.19
 p-value of test no 42                 :  7.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.69
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.74
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.22
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.08
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.41
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.33
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.55
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.63
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.49
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.15
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.22
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.43
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.30
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.82
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.79
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.11
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908179
   j =  2                              :            45906
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908443
   j =  2                              :            45774
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.90
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.70
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.41
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.73
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.84
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.00
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.19
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.07
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.71
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.39
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.66
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.50
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.41
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.33
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.02
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.96
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.38
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.11
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.90
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.72
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.40
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.06
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.38
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.39
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.21
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  558.28
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.12
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.75
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.06
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.43
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.60
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.56
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.47
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.01
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.92
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.09
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.01
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.68
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.31
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.38
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.97
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.37
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9932.23
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.48
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.87
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.20
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.28
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.26
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11713.21
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.02
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000010552
 
 Normal statistic for number of bits   :   0.083
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.21
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999926801
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 238                :    0.73
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.60
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:33.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35466
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    2.79
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     647
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.06
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.44
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.09
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.52
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.67
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.94
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.93
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.36
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.34
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.06
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.58
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.88
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.98
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.11
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.47
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.10
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.96
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908335
   j =  2                              :            45831
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908063
   j =  2                              :            45961
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.90
 p-value of test no 115                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.24
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.31
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.34
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.40
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.05
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.12
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 126                :  1.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    4.59
 p-value of test no 128                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.22
 p-value of test no 129                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.05
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.04
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17443.80
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.05
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.36
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.73
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.59
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.15
 p-value of test no 150                :    0.9921
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.55
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.78
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.16
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.59
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.33
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.00
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.56
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.38
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.22
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.58
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.03
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  569.62
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.67
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.13
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.02
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.26
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.47
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.46
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.70
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.78
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.64
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.33
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.38
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.03
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.21
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.26
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 188                :  6.5e-3
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.80
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.07
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.15
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.27
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.13
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.55
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.91
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.48
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.60
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.89
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11766.97
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.12
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000006457
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.79
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000005452
 
 Normal statistic for number of bits   :   0.043
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:10.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35467
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.15
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.35
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.58
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.90
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.96
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.49
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.35
 p-value of test no 52                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.71
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.12
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1577.32
 p-value of test no 56                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7148.58
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 58                 :    0.9932
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   50.29
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.73
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.48
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4976.57
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908634
   j =  2                              :            45683
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45466
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869466
   j =  1                              :        399909073
   j =  2                              :            45456
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.04
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 120                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.51
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.14
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.15
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.17
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.04
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.53
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.25
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.77
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.35
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17333.66
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.82
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.40
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.47
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.85
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.66
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.43
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.36
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.00
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.12
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.06
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.72
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.16
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.45
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.13
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.86
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.34
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.41
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.42
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.10
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.49
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.50
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.57
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.65
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.91
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.41
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4842.51
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.80
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.21
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.53
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.76
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.26
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.40
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.60
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.97
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4659.69
 p-value of test no 222                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.31
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.13
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.40
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.69
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.29
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.89
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000021262
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.88
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000122038
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.85
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:30.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35468
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9908
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    2.98
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.13
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.74
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.79
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.37
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.86
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.29
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.24
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.61
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.15
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  472.86
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.95
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6850.61
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.88
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.62
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.93
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5019.87
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907895
   j =  2                              :            46048
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45314
 p-value of test no 71                 :    0.9959
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869314
   j =  1                              :        399909373
   j =  2                              :            45312
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 84                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 85                 :  9.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.97e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.49
 p-value of test no 119                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.03
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.92
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.68
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.78
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.34
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.53
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 128                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.92
 p-value of test no 129                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.58
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.46
 p-value of test no 134                :  9.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.15
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17813.23
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.30
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.61
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.99
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.20
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.19
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.70
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.52
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.59
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.78
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.62
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.05
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.05
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.03
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.77
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.55
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.47
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.32
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.25
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.69
 p-value of test no 166                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.19
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.65
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  460.67
 p-value of test no 169                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.06
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.90
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.79
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.74
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.67
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.67
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.19
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.23
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.76
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.29
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.18
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.33
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.30
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4996.45
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.93
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.46
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11870.91
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.23
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999993782
 
 Normal statistic for number of bits   :  -0.049
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.91
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999994595
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.2e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35469
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1480
 p-value of test no 3                  :  1.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334600
   j =  1                              :        599997040
   j =  2                              :             1480
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    2.95
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.60
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.77
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.73
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.05
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.18
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.75
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.26
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.90
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.24
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.54
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.75
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.89
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.28
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.89
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5272.17
 p-value of test no 68                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907823
   j =  2                              :            46087
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46139
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870139
   j =  1                              :        399907724
   j =  2                              :            46135
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.52
 p-value of test no 115                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.54
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.16
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.20
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.58
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.02
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.74
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.02
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.82
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.29
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.11
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.25
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17187.84
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.79
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.84
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.32
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.30
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.69
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.16
 p-value of test no 153                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.03
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.62
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.45
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.64
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.57
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.45
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.76
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.40
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.61
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.75
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.20
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.72
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.99
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.28
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.15
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.08
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.34
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.37
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.49
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.33
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.43
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.03
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.91
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.08
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.05
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.75
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10143.59
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.32
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4782.41
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.58
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.43
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.01
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.87
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.75
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999949814
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.38
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999834323
 
 Normal statistic for number of bits   :   -1.31
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 238                :    0.22
 
 Sample variance                       :    2.25
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35470
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 3                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1253
 p-value of test no 12                 :    0.9988
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334373
   j =  1                              :        599997494
   j =  2                              :             1253
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5550
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4166
 p-value of test no 16                 :    0.9953
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 27                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    5.41
 p-value of test no 38                 :  1.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    5.90
 p-value of test no 39                 :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 41                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.96
 p-value of test no 46                 :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.93
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.80
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.13
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.44
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.81
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.60
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.65
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7257.81
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.45
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.79
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.38
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.75
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.85
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46026
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870026
   j =  1                              :        399907951
   j =  2                              :            46020
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45398
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869398
   j =  1                              :        399909209
   j =  2                              :            45388
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.01
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.56
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.18
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.47
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.43
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.26
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.97
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.15
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.54
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.71
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17407.86
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.93
 p-value of test no 146                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.11
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.36
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.60
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.92
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.67
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.99
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.62
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.02
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.38
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.56
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.12
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.77
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.98
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  393.75
 p-value of test no 163                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.76
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.85
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.78
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.72
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.46
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.80
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.61
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.28
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.76
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.50
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.17
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  262.84
 p-value of test no 175                :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.63
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.09
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   23.43
 p-value of test no 198                :  2.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.92
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.25
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.81
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.06
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.72
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.21
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.18
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.66
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.38
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.58
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.09
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000128842
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.03
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999874844
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.55
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:35.18
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35471
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 10                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.54
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.27
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.90
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.67
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.12
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.82
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.90
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.02
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.97
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.28
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.98
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.90
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.01
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.94
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45392
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869392
   j =  1                              :        399909216
   j =  2                              :            45392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908995
   j =  2                              :            45498
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 74                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 114                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.25
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.28
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.69
 p-value of test no 121                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.75
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.88
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.50
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.22
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.41
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.48
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    4.60
 p-value of test no 140                :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  181.19
 p-value of test no 141                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17255.71
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.28
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.30
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.49
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.55
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.48
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.47
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.30
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.46
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.90
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.69
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.18
 p-value of test no 157                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.06
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  184.38
 p-value of test no 159                :  3.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.14
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.90
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.19
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.65
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.83
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.56
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.03
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.09
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.25
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.51
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.12
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.95
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.27
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.95
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.19
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.09
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.46
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.19
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.69
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 200                :  5.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-3
 p-value of test no 201                :    0.9983
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 202                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  144.75
 p-value of test no 203                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 205                :    0.9919
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.69
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.00
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.21
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.66
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    6.23
 p-value of test no 225                :  8.2e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4573.91
 p-value of test no 226                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.67
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.04
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.59
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.54
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.92
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999844847
 
 Normal statistic for number of bits   :   -1.23
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.75
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000013465
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    2.53
 p-value of test no 239                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  96  HammingIndep, L=30, r=27        0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35472
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 33                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    3.21
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.88
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.62
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.74
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.13
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.47
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.17
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.03
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1300.57
 p-value of test no 56                 :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6808.42
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.98
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.14
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.40
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5180.59
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9992    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908563
   j =  2                              :            45714
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907896
   j =  2                              :            46046
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.00e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.51
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.17
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.49
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   14.41
 p-value of test no 122                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.13
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.95
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.08
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.48
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.88
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.17
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.02
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.33
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.41
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.71
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.78
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.50
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.44
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.06
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.99
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.07
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.81
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.22
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.39
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.61
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.30
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.71
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.45
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.51
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.19
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  320.94
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.25
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.93
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.45
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.95
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.97
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.00
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 183                :    0.42
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.61
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.15
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.74
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.90
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.83
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.25
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.58
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.77
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.92
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.43
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.57
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.49
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999863102
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.03
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999852596
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 242                :    0.9934
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  43  Permutation, t = 10             0.9992 
  62  WeightDistrib, r = 0            0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35473
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5525
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.99
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.31
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.12
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.47
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.56
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.28
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.78
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.24
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.94
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7423.63
 p-value of test no 57                 :  8.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.01
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.85
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.06
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.51
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5222.61
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45532
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869532
   j =  1                              :        399908939
   j =  2                              :            45526
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908049
   j =  2                              :            45971
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 99                 :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.41
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.76
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.18
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.02
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.80
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.49
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.21
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.81
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.37
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.96
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.97
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.37
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.66
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.07
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.58
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.75
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.86
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.27
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    9.04
 p-value of test no 153                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.35
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.27
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.69
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.70
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.92
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.28
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.96
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.18
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.05
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.56
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.67
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.29
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.52
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.24
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.70
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.30
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  324.20
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.44
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.22
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 201                :    0.85
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.51
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.72
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.84
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.85
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 218                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.09
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.96
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.72
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.65
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.44
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11505.93
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.10
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000169132
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.19
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000135505
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:00.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  37  Gap, r = 20                     8.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35474
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5340
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.78
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.66
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.36
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.48
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.24
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.07
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.14
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.70
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.37
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.51
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.26
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 60                 :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.02
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.06
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.31
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   90.92
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.98
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46275
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870275
   j =  1                              :        399907454
   j =  2                              :            46267
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908455
   j =  2                              :            45771
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.92
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.48
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.81
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.63
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.41
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.46
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.02
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.44
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
 p-value of test no 142                :    0.9962
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17730.36
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.43
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.24
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.99
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.85
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.15
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.71
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.55
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.44
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.82
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.65
 p-value of test no 160                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.59
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.57
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.82
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.01
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.99
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.87
 p-value of test no 166                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.11
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.62
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.58
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.84
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.93
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.59
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.46
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.08
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.33
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 185                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.82
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.67
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.56
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.48
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.04
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4719.75
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.45
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.40
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.99
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.66
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.00
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999777422
 
 Normal statistic for number of bits   :   -1.76
 p-value of test no 232                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.61
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000050008
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 238                :    0.88
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 245                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:40.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35475
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.39
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.27
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.46
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.24
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.65
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.88
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.94
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.40
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.47
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.93
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.35
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.11
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.18
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908442
   j =  2                              :            45776
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45965
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869965
   j =  1                              :        399908075
   j =  2                              :            45955
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.81
 p-value of test no 117                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.57
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.25
 p-value of test no 120                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.19
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.18
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.57
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.67
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.12
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.41
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.99
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.91
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.92
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.41
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.37
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.97
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.05
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.52
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.55
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.68
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.05
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.31
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.73
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.12
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.05
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.62
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.15
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.54
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.51
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.73
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.64
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.77
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.21
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.55
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.46
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.92
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.63
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.73
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.23
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.51
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.52
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.08
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.83
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.74
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   21.90
 p-value of test no 198                :  5.1e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.99
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.45
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.59
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.42
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.15
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.31
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.63
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.88
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.44
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12166.61
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.33
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999915011
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.28
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999990395
 
 Normal statistic for number of bits   :  -0.076
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    2.46
 p-value of test no 249                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 250                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 251                :    0.9941
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.71
 p-value of test no 253                :    0.9966
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:53.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35476
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9945
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5264
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7176
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.22
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    4.13
 p-value of test no 44                 :  7.6e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.31
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.83
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.52
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.53
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.10
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.82
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.97
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1344.56
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.85
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.25
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.83
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.98
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.40
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.21
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908331
   j =  2                              :            45830
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46147
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870147
   j =  1                              :        399907707
   j =  2                              :            46145
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.64
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.49
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.91
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.19
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.04
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.08
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.91
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17301.72
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.14
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.72
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.49
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.41
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.71
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.26
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.13
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.19
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.16
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.71
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.41
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.19
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.99
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  637.92
 p-value of test no 163                :  2.7e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.11
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.23
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.54
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.78
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.30
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.63
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.00
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.38
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.28
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4874.67
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.79
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.63
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.62
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.30
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.59
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.73
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.51
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4731.89
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.85
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.93
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.82
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.19
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.08
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.34
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000074728
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.81
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999893342
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    2.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35477
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  4.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7172
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    8.04
 p-value of test no 28                 :  1.2e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    5.11
 p-value of test no 32                 :  2.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    3.92
 p-value of test no 36                 :  9.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     344
 p-value of test no 37                 :  6.9e-3
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.01
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.86
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.55
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.76
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.71
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.19
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.15
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.05
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.82
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.88
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.77
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.61
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.62
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.65
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46167
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870167
   j =  1                              :        399907669
   j =  2                              :            46161
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46057
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870057
   j =  1                              :        399907893
   j =  2                              :            46043
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.94
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.91
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.94
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.28
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.33
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.44
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.40
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.65
 p-value of test no 135                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.92
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.06
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17322.33
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.69
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.12
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.40
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.43
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.83
 p-value of test no 150                :    0.9942
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.95
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.06
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.60
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.35
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.10
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  188.62
 p-value of test no 156                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.29
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.78
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.31
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.88
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.31
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.74
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.61
 p-value of test no 165                :  7.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.66
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.22
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.01
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  319.36
 p-value of test no 169                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.76
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.87
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.15
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.90
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.96
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.92
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.52
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.14
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.34
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 205                :    0.9950
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.15
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.11
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9772.78
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.78
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4771.78
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.54
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.43
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.37
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11728.90
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.28
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000048382
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.01
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999962228
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 250                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 251                :    0.01
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.53
 p-value of test no 253                :  5.6e-3
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              4.5e-4
  23  ClosePairs NP, t = 5            1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35478
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 12                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5324
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7115
 p-value of test no 15                 :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9936
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 41                 :    0.9958
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.16
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.24
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.05
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.75
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.89
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.60
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.09
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.01
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.51
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.87
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.95
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.09
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.52
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908583
   j =  2                              :            45698
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908189
   j =  2                              :            45901
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9967
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.61
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.45
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.22
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.31
 p-value of test no 123                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.11
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.56
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.70
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.11
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.56
 p-value of test no 136                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.37
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17537.31
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.66
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.10
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.81
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.40
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.29
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.54
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.17
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.15
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.70
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.27
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.00
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.51
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.87
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.98
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.12
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.74
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.86
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.84
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.54
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.03
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.86
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.57
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.00
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.38
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.23
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.50
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.84
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.71
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.58
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.36
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 188                :    0.13
 
 Sample variance                       :    2.75
 p-value of test no 189                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.30
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.25
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.63
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.00
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 214                :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10399.75
 p-value of test no 215                :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.62
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.78
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.45
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.53
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.83
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.41
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.86
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000047521
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.01
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000061486
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 253                :    0.88
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:46.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35479
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 5                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    3.65
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.00
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.88
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.03
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.87
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.22
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  474.64
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.21
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.48
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.33
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.97
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.57
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.98
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45860
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869860
   j =  1                              :        399908284
   j =  2                              :            45852
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45879
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869879
   j =  1                              :        399908244
   j =  2                              :            45875
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.46
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.37
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.73
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.87
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.40
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.00
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.09
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.14
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.13
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.02
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.78
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.56
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.12
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.52
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.25
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.90
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.77
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.08
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.54
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.09
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.00
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.18
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.33
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.90
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.29
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.87
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.83
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.76
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.27
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.23
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  479.40
 p-value of test no 166                :  6.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  468.28
 p-value of test no 167                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.06
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  304.82
 p-value of test no 169                :    0.9977
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.32
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.46
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.89
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.06
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.23
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.53
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.69
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.72
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.48
 p-value of test no 188                :  6.6e-3
 
 Sample variance                       :    1.24
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.82
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.93
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.60
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.54
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.50
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.70
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.80
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.95
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.03
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.49
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.38
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12184.67
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.21
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999919868
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.89
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999894098
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 242                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.73
 p-value of test no 243                :  3.2e-3
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:23.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)    6.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35480
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 28                 :    0.9928
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.42
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.11
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.91
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.59
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.48
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.48
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.59
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.34
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  353.84
 p-value of test no 55                 :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.27
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.09
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.79
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.66
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.00
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.45
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4866.64
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45396
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869396
   j =  1                              :        399909211
   j =  2                              :            45390
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46248
 p-value of test no 71                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870248
   j =  1                              :        399907508
   j =  2                              :            46240
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 77                 :    0.9949
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.42e-4
 p-value of test no 109                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.34
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.48
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.49
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.47
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.02
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   16.61
 p-value of test no 124                :    0.9985
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.22
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.82
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.35
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.45
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  108.35
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17019.94
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.44
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.77
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.74
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.24
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.66
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.49
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.56
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.64
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  576.77
 p-value of test no 158                :  9.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.07
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.86
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.27
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.21
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.17
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.63
 p-value of test no 165                :    0.9927
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.23
 p-value of test no 166                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.98
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.32
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.02
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.09
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.52
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.73
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.23
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.44
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.63
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.61
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.53
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.33
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10012.27
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.00
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.07
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.96
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.61
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.27
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.96
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.36
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.51
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000009100
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.97
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000065158
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.031
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:07.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35481
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5521
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.70
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    2.39
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.28
 p-value of test no 41                 :  7.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    5.44
 p-value of test no 42                 :  1.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     119
 p-value of test no 43                 :    0.9949
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.56
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.57
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.16
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.68
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.01
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.87
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6940.59
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.42
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.47
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.35
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.35
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4808.83
 p-value of test no 68                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908101
   j =  2                              :            45945
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45638
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869638
   j =  1                              :        399908728
   j =  2                              :            45630
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.47
 p-value of test no 117                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.64
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.22
 p-value of test no 120                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.34
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.92
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.01
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.44
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 127                :    0.9945
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.62
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.73
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.19
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.65
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.64
 p-value of test no 146                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.66
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.19
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.90
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.12
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.90
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.60
 p-value of test no 152                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.52
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.82
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.79
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.82
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.91
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.10
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.66
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.97
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.06
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.28
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.72
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.90
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.75
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.21
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5226.35
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.44
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.73
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.04
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.38
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.02
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.11
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.94
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.10
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.67
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.47
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.24
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.81
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.90
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.86
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.29
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.25
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.59
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.94
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3925.81
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12126.00
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.67
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.41
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999884009
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.49
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000053734
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 243                :    0.69
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 251                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    4.09
 p-value of test no 252                :  8.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.61
 p-value of test no 253                :  4.6e-3
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:45:20.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35482
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5280
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 27                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.47
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.60
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.73
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.38
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.38
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.36
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.74
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.33
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.71
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.64
 p-value of test no 59                 :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.69
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.12
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.81
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.54
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5040.64
 p-value of test no 68                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908066
   j =  2                              :            45967
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908172
   j =  2                              :            45902
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-4
 p-value of test no 112                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.02e-6
 p-value of test no 113                :    0.9974
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 114                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.38
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.71
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.42
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.86
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.39
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.44
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.03
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.10
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.84
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17180.80
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.26
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.61
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.25
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.34
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.39
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.27
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.01
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.93
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.60
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.40
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.24
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.36
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.06
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.88
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.90
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.01
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.97
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.81
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.74
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  455.30
 p-value of test no 166                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.22
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.00
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.72
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.77
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.33
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.51
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5066.86
 p-value of test no 173                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.14
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.37
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.83
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.37
 p-value of test no 178                :    0.9923
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.62
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.43
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.37
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.05
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.02
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.23
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.99
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.05
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.37
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12135.03
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.85
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.14
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999820439
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.16
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999889931
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.80e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:23.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35483
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.12
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    3.28
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.48
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.25
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.30
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.89
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.87
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.43
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.96
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.72
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.33
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.50
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.42
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.46
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.13
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908026
   j =  2                              :            45984
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46079
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870079
   j =  1                              :        399907845
   j =  2                              :            46073
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 116                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.69
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.04
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.99
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.03
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.61
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.65
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.66
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 128                :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
 p-value of test no 131                :    0.9976
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.09
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.89
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17251.14
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.43
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.06
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.31
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.41
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.91
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.23
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.50
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.63
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.53
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.80
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.41
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.26
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.53
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.10
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.41
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.38
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.23
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.86
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.33
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.83
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.76
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.63
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.47
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.70
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.76
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.97
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.35
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.87
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.60
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.66
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.55
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.38
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.28e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-4
 p-value of test no 194                :    0.9934
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.42
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.62
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.08
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.26
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.89
 p-value of test no 222                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.89
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3956.65
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.39
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.59
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11654.58
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.81
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999894269
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.25
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999928751
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:52.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35484
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4472
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.09
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.81
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.56
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.48
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.69
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.52
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.55
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.31
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.79
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.46
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.84
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.85
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.39
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4865.66
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45529
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869529
   j =  1                              :        399908942
   j =  2                              :            45529
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  5.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.40
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.50
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.16
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.27
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.43
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.90
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.02
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.77
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.30
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.16
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.24
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.46
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.30
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.56
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.36
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.97
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.49
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.71
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.10
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.05
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.91
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.12
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.69
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.50
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  399.45
 p-value of test no 163                :    0.9997    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.70
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.91
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.47
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.87
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.64
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.43
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.04
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.00
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.95
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.88
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.50
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.75
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.32
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -3.06
 p-value of test no 177                :    0.9989
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.11
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.12
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.87
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.28
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.67
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.68
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.76
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.67
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.83
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12124.05
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.07
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000097675
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.16
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999988895
 
 Normal statistic for number of bits   :  -0.088
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 J (L=1000, r=20)    0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35485
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4189
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 28                 :    0.9986
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.15
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.59
 p-value of test no 51                 :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.46
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.80
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.24
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.07
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.95
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.95
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.51
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.62
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.14
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.57
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45900
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869900
   j =  1                              :        399908201
   j =  2                              :            45898
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907731
   j =  2                              :            46127
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 6.86e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.68
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.53
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.75
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.72
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   13.44
 p-value of test no 125                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.96
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.93
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.36
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.65
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.31
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   57.17
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.08
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.79
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.50
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.62
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.35
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.57
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.66
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.51
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.39
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.81
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.16
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.03
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.29
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.77
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.20
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.91
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.26
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.51
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.24
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.61
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.10
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.93
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.12
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.53
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.44
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.93
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.63
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.72
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.40
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-4
 p-value of test no 193                :    0.9937
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.97
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 202                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  256.74
 p-value of test no 203                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.70
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.89
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.22
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
 p-value of test no 220                :    0.9953
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4626.19
 p-value of test no 222                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.16
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.33
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.85
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.76
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11937.64
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.13
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000051010
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.77
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000022510
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:56.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35486
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5499
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     837
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    3.32
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    2.77
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.35
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.04
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.22
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.64
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.15
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.41
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.64
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.20
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.31
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.58
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.34
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.81
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.35
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4826.15
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908550
   j =  2                              :            45722
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.82
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.44
 p-value of test no 120                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.53
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.12
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.66
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.87
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.26
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 130                :  2.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.56
 p-value of test no 133                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.10
 p-value of test no 134                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.07
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 138                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.85
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.30
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.23
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.36
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.14
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.38
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.47
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.07
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.19
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.54
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.86
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.64
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.30
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.17
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.00
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.19
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.48
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.89
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.04
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.13
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.19
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.36
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.32
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.05
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.00
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.59
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.30
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.26
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.77
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.81
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.53
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.20
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    2.63
 p-value of test no 189                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.97
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.29
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.25
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.01
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.80
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.38
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.89
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.09
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.04
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3878.93
 p-value of test no 228                :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11982.22
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.71
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.03
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000002275
 
 Normal statistic for number of bits   :   0.018
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.31
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000105526
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:08.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35487
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 5                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     560
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.80
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.45
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.56
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.07
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.22
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.21
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1568.18
 p-value of test no 56                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6831.01
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.90
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.36
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.66
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.31
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5281.62
 p-value of test no 68                 :  8.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908213
   j =  2                              :            45883
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908505
   j =  2                              :            45743
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 78                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
 p-value of test no 97                 :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.20
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.85
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.08
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.64
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.81
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.02
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.17
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.05
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.77
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 137                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.27
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17467.72
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.36
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.96
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.92
 p-value of test no 149                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.29
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.03
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.97
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.65
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.03
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.84
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.90
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.94
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.25
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.83
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.48
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.55
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.85
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.09
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.57
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.87
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.39
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.68
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.35
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.55
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.90
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.11
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.09
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.48
 p-value of test no 177                :    0.9934
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.49
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 194                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.14
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.60
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.09
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.79
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.62
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.66
 p-value of test no 217                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.93
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.85
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3985.61
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.57
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.20
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.79
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.34
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999950810
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.68
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999957971
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.76
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:50.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35488
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 16                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.38
 p-value of test no 35                 :  7.0e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.62
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.26
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.95
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.43
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.55
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.97
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  518.95
 p-value of test no 55                 :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.58
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.53
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.73
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.72
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.63
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.87
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5136.99
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45601
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908800
   j =  2                              :            45597
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46115
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870115
   j =  1                              :        399907776
   j =  2                              :            46103
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.70
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.21
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.78
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.23
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.70
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.35
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.85
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.19
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
 p-value of test no 142                :    0.9959
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 143                :  5.4e-3
 
 Anderson-Darling statistic = A2       :    5.34
 p-value of test no 144                :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :18030.81
 p-value of test no 145                :  7.2e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.64
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.48
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.35
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.78
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.48
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.71
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.66
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.75
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.80
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.11
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.20
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.90
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.90
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.21
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  104.34
 p-value of test no 162                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.20
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.10
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.10
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.47
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.32
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.45
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.92
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.34
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.83
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.92
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.87
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.22
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.09
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.84
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.78
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.65
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 201                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.80
 p-value of test no 203                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.17
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.36
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.33
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4863.66
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.53
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.65
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.53
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11438.97
 p-value of test no 229                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.95
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.42
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000018550
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.86
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999971885
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:37.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP, t = 9           7.0e-4
  73  GCD                             7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35489
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.79
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.29
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.86
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.90
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.39
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.84
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.76
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.85
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.75
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.96
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.69
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.65
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.30
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.64
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.95
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.40
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.51
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.74
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.09
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908813
   j =  2                              :            45589
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908257
   j =  2                              :            45864
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 81                 :    0.9990
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  6.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.98
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.99
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.44
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.72
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.71
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.35
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.40
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.98
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.20
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.91
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.27
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.26
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.00
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.18
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.22
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.47
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.80
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.00
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.33
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.93
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.72
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.40
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.92
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.35
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.37
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.96
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.20
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.20
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.77
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.30
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.01
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.27
 p-value of test no 165                :  5.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.99
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.02
 p-value of test no 167                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.38
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.04
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.00
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.21
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.05
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.01
 p-value of test no 174                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.95
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.59
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.57
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.02
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.30
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 209                :  2.2e-3
 
 Anderson-Darling statistic = A2       :    3.98
 p-value of test no 210                :  9.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10324.31
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9763.65
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -3.91e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.26
 p-value of test no 222                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.85
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.14
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.61
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.00
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.27
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.93
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999996701
 
 Normal statistic for number of bits   :  -0.026
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.36
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999906968
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
 p-value of test no 240                : 1 -  3.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    5.34
 p-value of test no 242                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.63
 p-value of test no 243                :  1.4e-4    *****
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:50.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  104  AutoCor, d=3, r=0               1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35490
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    4.09
 p-value of test no 24                 :  7.9e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     793
 p-value of test no 25                 :    0.9999    *****
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.94
 p-value of test no 28                 :  9.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 29                 :    0.9970
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.05
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.81
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.46
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.85
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.79
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.76
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.18
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.97
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.34
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.13
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.01
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.24
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.03
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908511
   j =  2                              :            45743
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908550
   j =  2                              :            45719
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.44
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.48
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.74
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.31
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.57
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.43
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 139                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.11
 p-value of test no 141                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.37
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.66
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.09
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.73
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.13
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.01
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.38
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.87
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.00
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.34
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.92
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.37
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.29
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.04
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.78
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.07
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.51
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.17
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.96
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.30
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4965.25
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.89
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.63
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.93
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.35
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.16
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.53
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.02
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.43
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.84
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.51
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.00
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10137.10
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.94
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.62
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.56
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.55
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.26
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.27
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.56
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999809372
 
 Normal statistic for number of bits   :   -1.51
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.76
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000031246
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NJumps, t = 3        0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35491
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5511
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9969
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.06
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.48
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.70
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.63
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.45
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.54
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.73
 p-value of test no 52                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.76
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.13
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.35
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.21
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6870.84
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 58                 :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.65
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.70
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.91
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5175.03
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908013
   j =  2                              :            45992
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908723
   j =  2                              :            45637
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 76                 :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.15e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 119                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.87
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.77
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.06
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.97
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.68
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.09
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.13
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.81
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.49
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17695.08
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.26
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.92
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.95
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.42
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.26
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.71
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.18
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.40
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.40
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.13
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.61
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.68
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.21
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.05
 p-value of test no 161                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.17
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.74
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.54
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.32
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.44
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.81
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.08
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.93
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.70
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.28
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.73
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.57
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.37
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.68
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.56
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.93
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.32
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.90
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.07
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.41
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.68
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5048.94
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.64
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.61
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.06
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.78
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.56
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999849224
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 232                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.97
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999903587
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 251                :  1.0e-3
 
 Anderson-Darling statistic = A2       :    5.67
 p-value of test no 252                :  1.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.18
 p-value of test no 253                :  7.3e-4    *****
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  106  AutoCor, d=3, r=27              7.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35492
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 7                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1507
 p-value of test no 10                 :  7.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334627
   j =  1                              :        599996986
   j =  2                              :             1507
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 12                 :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.71
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.94
 p-value of test no 46                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.52
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.10
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.03
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.22
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.22
 p-value of test no 51                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.60
 p-value of test no 53                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.33
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.01
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.99
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.55
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.21
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.36
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.53
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.69
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45919
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869919
   j =  1                              :        399908163
   j =  2                              :            45917
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46136
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870136
   j =  1                              :        399907730
   j =  2                              :            46132
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.31
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.52
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.93
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.08
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.74
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.39
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.51
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.13
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.45
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.49
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.19
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.73
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.35
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.77
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.62
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.88
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.09
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.58
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.60
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.46
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.33
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.24
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.83
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.65
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.29
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.79
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.13
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.92
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.54
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.22
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.31
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.42
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.61
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.04
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.30
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.75
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.59
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.70
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.25
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.15
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.11
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 183                :    0.33
 
 Sample variance                       :    2.26
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.32
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.84
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.07
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 208                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10238.61
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.98
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.93
 p-value of test no 216                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.41
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.01
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.42
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.11
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11651.05
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.29
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.24
 p-value of test no 231                :    0.9918
 
 
 -----------------------------------------------
 Total number of bits:  7999969992
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.01
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000028831
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:22.42
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           7.5e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35493
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 8                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.36
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    4.46
 p-value of test no 44                 :  5.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.28
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.37
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.20
 p-value of test no 50                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.54
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.65
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.31
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.26
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.20
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1345.21
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.13
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.18
 p-value of test no 61                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.35
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.66
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.03
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908191
   j =  2                              :            45903
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45888
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869888
   j =  1                              :        399908227
   j =  2                              :            45882
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.15
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.08
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.62
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.11
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.58
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.58
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.04
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 132                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.46
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.48
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.93
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17231.41
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.88
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.00
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.40
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.53
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.96
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.08
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.92
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.88
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.68
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.51
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.08
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.71
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.10
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.27
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.67
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.25
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.36
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.38
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4870.39
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.94
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.53
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.78
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.41
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.85
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.63
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.15
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.36
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.095
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.85
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 195                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.13
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.18
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.31
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.37
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.39
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 221                :    0.9984
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.97
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.37
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3972.62
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.35
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.85
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.10
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.45
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999944582
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.31
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000059755
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  30  CouponCollector, r = 0          0.9991 
  85  Fourier3, r = 27                0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35494
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1500
 p-value of test no 9                  :  1.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334620
   j =  1                              :        599997000
   j =  2                              :             1500
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.86
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.46
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.16
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.56
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.30
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.20
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.48
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.92
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.70
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.07
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.67
 p-value of test no 65                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.97
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.19
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.20
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908231
   j =  2                              :            45877
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908234
   j =  2                              :            45883
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.98
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.66
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.24
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.35
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.61
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.89
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.81
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17663.68
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.77
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.72
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.37
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.14
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.86
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.71
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.60
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.12
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.42
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.18
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.09
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.33
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.34
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.60
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.98
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.80
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.13
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.23
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.55
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.82
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.27
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.49
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.69
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.42
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5202.02
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.32
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.23
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.09
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.85
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.98
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.56
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9936.90
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9696.91
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.34
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.03
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.89
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.92
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12144.76
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.25
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.33
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999885389
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.72
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000091363
 
 Normal statistic for number of bits   :    0.72
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 243                :    0.02
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    2.11
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:47.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           1.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35495
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7036
 p-value of test no 18                 :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.44
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.27
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.78
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.09
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.20
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.69
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.49
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.99
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.32
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.74
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.00
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.37
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.72
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.42
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.51
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.31
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4939.21
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908447
   j =  2                              :            45772
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46056
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870056
   j =  1                              :        399907890
   j =  2                              :            46052
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.17
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.18
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.80
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.62
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.83
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.82
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.39
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.86
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.57
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.42
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.25
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.30
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.10
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.78
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.58
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.55
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.52
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.35
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.14
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.16
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.76
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.51
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.04
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.92
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.40
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  578.53
 p-value of test no 163                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.69
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.77
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.58
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.97
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.35
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.23
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.66
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.01
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.22
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.63
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.89
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.67
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.62
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.61
 p-value of test no 198                :    0.9907
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.14
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.39
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.39
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.23
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.53
 p-value of test no 218                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.84
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.30
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4315.05
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.99
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.61
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.41
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.31
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999969965
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.84
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000106636
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.68
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:20.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35496
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4501
 p-value of test no 16                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     836
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 33                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.14
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.52
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.58
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.58
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.27
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.69
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.80
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.43
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7022.82
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.63
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.82
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.23
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.90
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.36
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908031
   j =  2                              :            45980
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907812
   j =  2                              :            46091
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 84                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    5.41
 p-value of test no 85                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.39
 p-value of test no 116                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.30
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.93
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.07
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.27
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.52
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.74
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.59
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.17
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.25
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17131.22
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.51
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.58
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.95
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.15
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.87
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.98
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.25
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.41
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.81
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.09
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.41
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.07
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.39
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.64
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.76
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.24
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.11
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.85
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.66
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.84
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.18
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.65
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.70
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.28
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.54
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.19
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.62
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.15
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.30
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.00
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.96
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 188                :    0.95
 
 Sample variance                       :    2.16
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.92
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.08
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9769.10
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.75
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4637.77
 p-value of test no 222                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.98
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3871.18
 p-value of test no 227                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.91
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12060.15
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.15
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.99
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000078022
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.58
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000075181
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35497
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7132
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.68
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.96
 p-value of test no 50                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.02
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.34
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.88
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.92
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.92
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.45
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6850.90
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.67
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.41
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.07
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.31
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908672
   j =  2                              :            45658
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45605
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869605
   j =  1                              :        399908795
   j =  2                              :            45595
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.77
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.12
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.53
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.43
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.74
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.77
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.89
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.61
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.29
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.88
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.82
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.54
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.35
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.07
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.07
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.96
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.51
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.45
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.85
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.05
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.46
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.13
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.36
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.35
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.79
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.33
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.92
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.68
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.41
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.73
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.75
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.26
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.59
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.57
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.66
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.17
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.48
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.07
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.77
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.94
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.72
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.29
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 180                :  7.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    6.31
 p-value of test no 182                :  7.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.20
 p-value of test no 183                :    0.9993    *****
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.99
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.44
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.62
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.51
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.90
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.70
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4860.84
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4712.00
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.65
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.73
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11608.76
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12143.69
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.00
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999859793
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.49
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999905312
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
 p-value of test no 241                :    0.9939
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.31
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:07.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0                0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35498
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 14                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9961
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.36
 p-value of test no 35                 :  6.1e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.60
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.94
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.91
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.56
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  490.87
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.29
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.01
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.33
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.38
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.92
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.58
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908465
   j =  2                              :            45763
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 73                 :  1.1e-3
 
 Anderson-Darling statistic = A2       :    4.98
 p-value of test no 74                 :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  4.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
 p-value of test no 103                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.31
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.09
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.37
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.26
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.46
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.35
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.20
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.09
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.24
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17688.53
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.11
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.01
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.63
 p-value of test no 148                :    0.9946
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.61
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.89
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.03
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.87
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.87
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.49
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.32
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.34
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.37
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.49
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.02
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.63
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.17
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.52
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.21
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.14
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.35
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.78
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.07
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.46
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.06
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.02
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.69
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.41
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.25
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 183                :    0.20
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.64
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.56
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.93
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.03
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.09
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
 p-value of test no 209                :    0.9958
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9674.21
 p-value of test no 211                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.42
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.25
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.32
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.12
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.80
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12266.25
 p-value of test no 229                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.45
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.03
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000006445
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.10
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000031672
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 3.84e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.64
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35499
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.66
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.33
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.30
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.39
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.11
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.01
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.29
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.21
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.77
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.71
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.55
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.14
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.59
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.56
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.79
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5001.68
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908555
   j =  2                              :            45721
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907730
   j =  2                              :            46129
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.80
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.56
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.84
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.48
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.04
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.07
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.30
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.95
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.75
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.17
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17514.14
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.21
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.07
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.21
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.74
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.03
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.20
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.15
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.92
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.28
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.44
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.19
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.79
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.52
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.68
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.92
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.40
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.37
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.47
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.30
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.41
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.18
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.26
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.69
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.75
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.35
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.58
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.97
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.42
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.27
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.15
 p-value of test no 178                :  5.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 194                :    0.01
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 195                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.39
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.21
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.46
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.68
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.94
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.52
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.18
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.33
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.61
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.51
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.56
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000005605
 
 Normal statistic for number of bits   :   0.044
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.27
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000032932
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 238                :    0.54
 
 Sample variance                       :    0.44
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:54.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35500
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 9                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    3.50
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.34
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.80
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.69
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.34
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.87
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1362.26
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6918.69
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.67
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.01
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.19
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.77
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5083.73
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45585
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869585
   j =  1                              :        399908838
   j =  2                              :            45569
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45971
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869971
   j =  1                              :        399908060
   j =  2                              :            45967
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.34
 p-value of test no 115                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.37
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.29
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.81
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.56
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.94
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.48
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.19
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.52
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.67
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17553.20
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.42
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.69
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.74
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.10
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   64.52
 p-value of test no 151                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.16
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.70
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.85
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.01
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  603.34
 p-value of test no 158                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.77
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.64
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.07
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.41
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.39
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.96
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.20
 p-value of test no 165                :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.12
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.42
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.51
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.63
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.85
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.85
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.51
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4789.77
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.80
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.23
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.26
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.11
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.82
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.78
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.67
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4814.77
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.51
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.54
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.51
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11992.19
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.86
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.90
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000108643
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.81
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000007282
 
 Normal statistic for number of bits   :   0.058
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 236                :    0.9977
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    2.06
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:51.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35501
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5526
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.41
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.38
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.46
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.67
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.51
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.21
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.14
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6852.93
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.19
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.33
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.62
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.16
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.56
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907906
   j =  2                              :            46038
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908101
   j =  2                              :            45939
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-6
 p-value of test no 113                :    0.9972
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.15
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.82
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.73
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.72
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.27
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.39
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.15
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 139                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.88
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.84
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.48
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.48
 p-value of test no 148                :    0.9903
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.81
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.68
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.49
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.61
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.36
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.71
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.43
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.95
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  571.04
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.50
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.57
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.70
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.23
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.65
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.41
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.80
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.11
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.51
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.41
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.76
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.21
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.00
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.21
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.39
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  310.66
 p-value of test no 174                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.11
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.51
 p-value of test no 178                :    0.9981
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.34
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 195                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.21
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.33
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.67
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.99
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.52
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.70
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4712.52
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.52
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.26
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.40
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.01
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999883304
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.13
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999881909
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.018
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.90
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:41.03
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35502
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.23
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.59
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.58
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.77
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.60
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.15
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.86
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.48
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.71
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7115.64
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.40
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
 p-value of test no 62                 :    0.9963
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.03
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.53
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.04
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45981
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869981
   j =  1                              :        399908043
   j =  2                              :            45971
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45582
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869582
   j =  1                              :        399908837
   j =  2                              :            45580
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
 p-value of test no 72                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.30
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.86
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.28
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.76
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.83
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.76
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.09
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.49
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.99
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.29
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.21
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.49
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.24
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.32
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.92
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.66
 p-value of test no 151                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.16
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.17
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.02
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.10
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.57
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.53
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.01
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.38
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.28
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.08
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.05
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.20
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.15
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.11
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.53
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.71
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.61
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.13
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.16
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.39
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.93
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.26
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.06
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.28
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.80
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.48
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.92
 p-value of test no 203                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.31
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10172.75
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.23
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.97
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.93
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.92
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12026.72
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.11
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.49
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000253258
 
 Normal statistic for number of bits   :    2.00
 p-value of test no 232                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000014359
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:25.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35503
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4445
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.12
 p-value of test no 46                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.78
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.48
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.66
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.16
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.75
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.32
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.07
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.20
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7135.06
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.31
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.23
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.99
 p-value of test no 66                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.69
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.74
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45916
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869916
   j =  1                              :        399908170
   j =  2                              :            45912
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46095
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870095
   j =  1                              :        399907814
   j =  2                              :            46087
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 78                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.24
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.62
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.67
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.03
 p-value of test no 122                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.24
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.42
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.82
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.85
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.32
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.02
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.36
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.15
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.90
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.38
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.64
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.18
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.86
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.51
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.87
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.88
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.86
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.97
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.04
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.20
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.95
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.00
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.36
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.94
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.99
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.92
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.30
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.14
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.25
 p-value of test no 175                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.19
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.18
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.29
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.72
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.85
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.95
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.06
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9823.38
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.06
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.02
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.34
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.93
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.20
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11871.72
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.96
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000069238
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.59
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999977975
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35504
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4567
 p-value of test no 17                 :  2.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.62
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.38
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.06
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.30
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.26
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.39
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.97
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.46
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.37
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.20
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.30
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.62
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.06
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.34
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46240
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870240
   j =  1                              :        399907522
   j =  2                              :            46236
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907927
   j =  2                              :            46029
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 77                 :    0.9939
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 91                 :    0.9972
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 102                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 103                :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.16
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.16
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.92
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.17
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.48
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.49
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.29
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.77
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 134                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.65
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 138                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  168.84
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.07
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.20
 p-value of test no 146                :    0.9966
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.52
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.33
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.72
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.43
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.09
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.93
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.54
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.47
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.35
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.58
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.23
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.51
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.39
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.31
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.77
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.47
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.80
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.95
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.46
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.34
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.80
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.60
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.94
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.76
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.61
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.80
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.91
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.01
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.82
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.45
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.14
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.48
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.24
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5016.77
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.43
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.71
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4304.63
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.66
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.33
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.53
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000028303
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.71
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000090031
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:35.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35505
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 10                 :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.63
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.77
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.67
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    3.39
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.13
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.78
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.52
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   85.63
 p-value of test no 51                 :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.32
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.60
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.81
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.09
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.00
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7092.03
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.58
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.89
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.79
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.69
 p-value of test no 67                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4893.71
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907985
   j =  2                              :            46006
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908053
   j =  2                              :            45963
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.37
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.26
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.73
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.21
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.27
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.67
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.62
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.08
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.26
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.25
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.84
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.32
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.54
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.99
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.32
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.32
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.74
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.54
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.71
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.89
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.37
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.29
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.55
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.07
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.21
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.35
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.90
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.75
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.42
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.80
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.76
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.06
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.62
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.71
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.47
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.07
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4966.44
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.51
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.71
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.36
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.65
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.67
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.37
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 199                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.48
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.38
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.95
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.11
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.22
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.53
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.29
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.23
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.08
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12060.78
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.60
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000081310
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.76
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999962684
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 253                :    0.89
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:11.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35506
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.74
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.60
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.35
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.46
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.32
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.50
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7209.88
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.89
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.30
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.86
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.43
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.03
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46336
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870336
   j =  1                              :        399907332
   j =  2                              :            46328
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908093
   j =  2                              :            45949
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.61
 p-value of test no 115                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.92
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.48
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.93
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.62
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.22
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   14.88
 p-value of test no 125                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.91
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.61
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.84
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17645.66
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.95
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.85
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.89
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.95
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.76
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.86
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.01
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.97
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.33
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.29
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.77
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.10
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.01
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.68
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.01
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.50
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.41
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.21
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.75
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.44
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5198.37
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.29
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.11
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.63
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.95
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.61
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.14
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.56
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.10
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.32
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.62
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.41
 
 Sample variance                       :    2.75
 p-value of test no 184                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.26
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.56
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.76
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.52
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.09
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 217                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4708.80
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5023.35
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.84
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.97
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.96
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.03
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.74
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999949409
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.04
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000156760
 
 Normal statistic for number of bits   :    1.24
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.64
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    2.68
 p-value of test no 254                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:00.03
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35507
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 4                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 27                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     345
 p-value of test no 37                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.03
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.44
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.51
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.89
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.03
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.64
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.00
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.35
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.87
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.38
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.68
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.87
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.05
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.63
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907990
   j =  2                              :            46002
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907904
   j =  2                              :            46042
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.92
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.34
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.62
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.30
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.78
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.55
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.39
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.96
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.86
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17525.89
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.90
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.21
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.60
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.48
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.49
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.97
 p-value of test no 151                :  7.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.05
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.68
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.01
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.94
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.34
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.73
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.41
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.10
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.86
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.92
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.00
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.68
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.03
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.81
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.14
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  429.23
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.87
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.74
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.46
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.21
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  301.65
 p-value of test no 174                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.04
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.93
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.42
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.36
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.69
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.50
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.87
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.42
 p-value of test no 216                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.28
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.36
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.14
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.15
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.75
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.33
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.12
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999984356
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.03
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999989891
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:08.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35508
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.44
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.61
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.54
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.51
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.80
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  179.70
 p-value of test no 54                 :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.87
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1384.93
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.38
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.97
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.32
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.85
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.14
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908352
   j =  2                              :            45818
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908580
   j =  2                              :            45701
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 73                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.72
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.81
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.78
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.17
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.41
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.96
 p-value of test no 125                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.82
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.97
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.089
 p-value of test no 135                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.19
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17751.69
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.45
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.21
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.57
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.74
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.63
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.91
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.37
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.64
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.84
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.52
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.23
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.09
 p-value of test no 161                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.60
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.11
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.05
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.70
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.22
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.97
 p-value of test no 167                :  4.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.37
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.89
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.78
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.24
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.76
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.35
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.57
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.68
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.56
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.07
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.38
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.48
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.08
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.10
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10153.76
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4657.28
 p-value of test no 222                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.55
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.76
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.76
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.18
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.45
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.51
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999982355
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.44
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000177358
 
 Normal statistic for number of bits   :    1.40
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 235                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:16.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35509
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.46
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.60
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.90
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.15
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.01
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.89
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.58
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.99
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.22
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.94
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6874.73
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.60
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.00
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.14
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.48
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.33
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46178
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870178
   j =  1                              :        399907644
   j =  2                              :            46178
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908204
   j =  2                              :            45895
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.4e-3
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 92                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.16
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.89
 p-value of test no 121                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.12
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.89
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.98
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.57
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.72
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.61
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.25
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.64
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.28
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.39
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.60
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.11
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 155                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.57
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.98
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.72
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.75
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.23
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.92
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.12
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.90
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.72
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.53
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.30
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.45
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.00
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.21
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.86
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.07
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.37
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  443.30
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.83
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 185                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 187                :  3.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.02
 p-value of test no 188                :    0.9987
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.45
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.00
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9701.15
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.10
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.094
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.09
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.21
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4188.02
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4293.91
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.32
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.37
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.28
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999840116
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.75
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000114430
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:57.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35510
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7168
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    2.33
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.45
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.73
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.29
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.34
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.50
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.42
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.26
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.76
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.06
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.07
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.45
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6897.51
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.50
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.10
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.17
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.97
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.00
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908092
   j =  2                              :            45951
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908576
   j =  2                              :            45703
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.23
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.75
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.92
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.50
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.51
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.87
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.34
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.10
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17596.96
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.90
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.76
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.82
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.23
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.77
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.13
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.90
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.52
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.75
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.85
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.94
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.76
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.19
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.43
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.10
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.72
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.57
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.07
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.17
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.98
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5186.35
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.51
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.87
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.02
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.53
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5218.68
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.99
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.53
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.29
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.99
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.10
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.41
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.85
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.82
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.93
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5061.46
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 223                :  2.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    7.23
 p-value of test no 225                :  2.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4593.52
 p-value of test no 226                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.30
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.31
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12132.42
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.44
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.89
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999935213
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.74
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000040993
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 240                :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:02.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35511
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 9                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5552
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.60
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.18
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.02
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.50
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.18
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.50
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.65
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.60
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.11
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.18
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.43
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.27
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.92
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.45
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.22
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.05
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908552
   j =  2                              :            45715
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.06
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.46
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.34
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.15
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.40
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.00
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.48
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17525.98
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.45
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.55
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.99
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.44
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.66
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.13
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.29
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.49
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.23
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.92
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.37
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.37
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.58
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.13
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.93
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.09
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.86
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.97
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.90
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.93
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.83
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.88
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.30
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.85
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.80
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.63
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.88
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.18
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.10
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.34
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.62
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.19
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 204                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.73
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.65
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.60
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 219                :  8.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 220                :    0.99
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4658.08
 p-value of test no 222                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.96
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.30
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.26
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.20
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.45
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.67
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999930674
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.25
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000085480
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 245                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 253                :    0.44
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:16.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35512
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    3.81
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.49
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.87
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.30
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.53
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.60
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.74
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.43
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.92
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.41
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.55
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.06
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.01
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.13
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.52
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45565
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869565
   j =  1                              :        399908871
   j =  2                              :            45563
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908715
   j =  2                              :            45638
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.84
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.69
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.34
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.50
 p-value of test no 122                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.41
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.29
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.61
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.54
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.48
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.91
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.53
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.74
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.98
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.43
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.62
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.91
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.84
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.27
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.39
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.73
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.54
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.65
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.20
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.10
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.27
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.24
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.52
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.83
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.56
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.56
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.65
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.23
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.80
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.10
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.68
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.50
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.81
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.63
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.44
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.92
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.34
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.57
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.53
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.69
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.91
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9665.50
 p-value of test no 211                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.94
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.65
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.39
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.34
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.72
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.99
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.01
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.14
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000002827
 
 Normal statistic for number of bits   :   0.022
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.65
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999890339
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.72
 p-value of test no 244                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:12.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35513
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.54
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     180
 p-value of test no 43                 :  9.4e-3
 
 Stat. AD (mNP2)                       :    3.93
 p-value of test no 44                 :  9.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.66
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.33
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.27
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.45
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.52
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.78
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7343.60
 p-value of test no 57                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.44
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.37
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.40
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.03
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.49
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908522
   j =  2                              :            45733
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45550
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869550
   j =  1                              :        399908902
   j =  2                              :            45546
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.11e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -5.27e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.07
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.83
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.45
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.50
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.24
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.63
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.74
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.80
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.85
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.88
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.24
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.52
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.36
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.49
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.66
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.21
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.47
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.44
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.71
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.68
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.01
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.79
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.78
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.05
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.05
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.57
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.86
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.18
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.62
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.95
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.24
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.72
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.71
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.98
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.08
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.65
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.55
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.42
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.84
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.37
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.53
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.16
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.024
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.11
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.93
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.03
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.76
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.40
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.18
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.75
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.94
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.96
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.51
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   78.42
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000022441
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.01
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999973679
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 250                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 252                :  7.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 253                :    0.9920
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:14.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35514
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 21                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 30                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.71
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.75
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.83
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.32
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.47
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.92
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.83
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.00
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.74
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1430.09
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.55
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.09
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.39
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.26
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.76
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.89
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45761
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869761
   j =  1                              :        399908481
   j =  2                              :            45755
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908467
   j =  2                              :            45756
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 87                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 88                 :  2.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  1.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.68e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.71
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.54
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.34
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.23
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.41
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.81
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.97
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   21.93
 p-value of test no 129                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.09
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.93
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17404.03
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.29
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.96
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.29
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.10
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.59
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.50
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.45
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.24
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.44
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.73
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.71
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.11
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.82
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.48
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.12
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.15
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.72
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.06
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.15
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.76
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.98
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.27
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.19
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.71
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.49
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.58
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.05
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.45
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.01
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.67
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.21
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-4
 p-value of test no 185                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 188                :  4.9e-3
 
 Sample variance                       :    1.60
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.52
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.53
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.60
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10078.71
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.72
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.40
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.08
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.64
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.24
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.44
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.42
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.57
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999967907
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.58
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999961883
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.38
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:28.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35515
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 4                  :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.84
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.39
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.89
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.28
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.97
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.96
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.10
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.52
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.52
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.77
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1398.10
 p-value of test no 56                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.51
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.72
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.03
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.68
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.84
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.05
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45747
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869747
   j =  1                              :        399908508
   j =  2                              :            45743
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908155
   j =  2                              :            45915
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.68
 p-value of test no 117                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.81
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.09
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.37
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.14
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.09
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.88
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.03
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.54
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 139                :    0.9919
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.92
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.85
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.66
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.99
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.08
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.13
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.06
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.62
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.14
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.63
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.15
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.87
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.57
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.97
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.27
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.83
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.90
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.57
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.92
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.32
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  454.92
 p-value of test no 169                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.23
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.13
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.93
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.48
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.25
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.34
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.77
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.88
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.13
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.25
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.01
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10084.18
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.65
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.95e-4
 p-value of test no 220                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4662.26
 p-value of test no 222                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.48
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.45
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.53
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.22
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.24
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.11
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999916388
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.86
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000092662
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.74e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:57.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35516
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.09
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.67
 p-value of test no 49                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.47
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.32
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.46
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.19
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.28
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.62
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.92
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.79
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   88.13
 p-value of test no 67                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.94
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907800
   j =  2                              :            46097
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.47
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.35
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.46
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.95
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.14
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.56
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.98
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.08
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.70
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.13
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.60
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.20
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.36
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.64
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.94
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.89
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 155                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.56
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.29
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.68
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.31
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.01
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.47
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.14
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.06
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.54
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.65
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.55
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.77
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.86
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.25
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.34
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.45
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.63
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.62
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.40
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.19
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.20
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.03
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.41
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.70
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.53
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.04
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.00
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4108.51
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.59
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.73
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.64
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000061222
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.43
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000016393
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.20
 p-value of test no 239                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 248                :    0.16
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:10.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35517
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 11                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.04
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.17
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.83
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.64
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.49
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.29
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.68
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.83
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6837.47
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.42
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.90
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.28
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.44
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5145.44
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908000
   j =  2                              :            45994
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45946
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869946
   j =  1                              :        399908111
   j =  2                              :            45940
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 115                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.58
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.37
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.84
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.97
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.55
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.32
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.45
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.36
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.74
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.07
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.87
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.92
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.46
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.08
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.99
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.35
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.58
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.26
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.98
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.51
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.08
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.41
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.42
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.34
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.76
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.58
 p-value of test no 164                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.88
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.90
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.67
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.58
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.00
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.41
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.49
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.78
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.37
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.12
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.42
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.76
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.78
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.80
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.21
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.40
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.37
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.80
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.42
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.02
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.43
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.80
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.53
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.39
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.48
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999869681
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.52
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000069283
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:10.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35518
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 9                  :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7483
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.64
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 26                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.13
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.00
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.01
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.49
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.44
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.06
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.88
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6863.35
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.68
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.76
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.22
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.22
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45603
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869603
   j =  1                              :        399908796
   j =  2                              :            45599
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908676
   j =  2                              :            45653
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.80
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.45
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.81
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.42
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.95
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.54
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.70
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.49
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.47
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.052
 p-value of test no 135                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.99
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17339.08
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.73
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.61
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.30
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.35
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.13
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.45
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.41
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.96
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.93
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.82
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.72
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.56
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.42
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.61
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.66
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.99
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.70
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.39
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.96
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.92
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.50
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.50
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.47
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.51
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.42
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.11
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.17
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.95
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.89
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.77
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.52
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.98
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.96
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.70
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.17
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.39
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4958.76
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.41
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.83
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.62
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.25
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.46
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000023548
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.91
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000115672
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:53.92
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35519
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7179
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 39                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.19
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.84
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.33
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.38
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.19
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.04
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.01
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.80
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.44
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.53
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.95
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.52
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.43
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.01
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.59
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907931
   j =  2                              :            46030
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45948
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869948
   j =  1                              :        399908108
   j =  2                              :            45940
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.19
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.26
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.97
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.47
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.74
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.20
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.81
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.13
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.27
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.74
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.09
 p-value of test no 135                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.12
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.83
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.95
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.59
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.74
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.98
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.92
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.51
 p-value of test no 151                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.84
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.25
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.97
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.40
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.42
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.16
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.87
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.13
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.52
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.21
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.79
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.59
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.20
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.58
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.26
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.47
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.75
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.33
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.78
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.77
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  468.17
 p-value of test no 174                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.74
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.20
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.56
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-3
 p-value of test no 193                :    0.9907
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.81
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.38
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.16
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.47
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.51
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.35
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.08
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5087.11
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.98
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.20
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.84
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.10
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.72
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000064981
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.24
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000074197
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:45.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35520
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4519
 p-value of test no 16                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 20                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7116
 p-value of test no 21                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    2.30
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     332
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    2.92
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.86
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.48
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.32
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.93
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.00
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.07
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.34
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.61
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1537.86
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7157.87
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.20
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.32
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.34
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.17
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5025.25
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45433
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869433
   j =  1                              :        399909138
   j =  2                              :            45425
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45712
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869712
   j =  1                              :        399908579
   j =  2                              :            45706
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.07e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.46
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.48
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.83
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.95
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.27
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.30
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.26
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.36
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.09
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.06
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17312.00
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.64
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.35
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.24
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.97
 p-value of test no 150                :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.20
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.02
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.83
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.61
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.17
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.53
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.59
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.88
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.68
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.55
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.44
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.99
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.72
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.86
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.10
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.12
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.00
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.35
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.52
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.23
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.31
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.88
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.33
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.77
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.29
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.75
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.74
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.14
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.27
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 225                :    0.9901
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.16
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.13
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3983.44
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.91
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.41
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.22
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999836168
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.08
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999943373
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.64
 p-value of test no 246                :  8.8e-5    *****
 
 Anderson-Darling statistic = A2       :    5.45
 p-value of test no 247                :  1.9e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.78
 p-value of test no 248                :  2.7e-3
 
 Sample variance                       :    0.31
 p-value of test no 249                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    2.02
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:39.67
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35521
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 5                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 12                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.78
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.02
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.96
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.78
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.78
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.16
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.83
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.90
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.89
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.36
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.65
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.69
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4902.40
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45518
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869518
   j =  1                              :        399908971
   j =  2                              :            45504
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907606
   j =  2                              :            46191
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.84
 p-value of test no 115                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.59
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.94
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.51
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.12
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.23
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.94
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.21
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.22
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.52
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 143                :    0.9962
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17047.35
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.99
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.67
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.26
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.70
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.82
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.60
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.49
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.62
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.97
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.31
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.89
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.43
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.35
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.00
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.91
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.14
 p-value of test no 166                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.69
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.62
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.82
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  254.30
 p-value of test no 170                :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.58
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.26
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.16
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.46
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.01
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.55
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.45
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 188                :    0.25
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
 p-value of test no 191                :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.86
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.60
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.04
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.58
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.81
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10272.27
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.28
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.45e-3
 p-value of test no 223                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5106.98
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.35
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.03
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11690.28
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11610.92
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.28
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000025603
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.07
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000064621
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:30.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35522
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 10                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5528
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    2.18
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    3.60
 p-value of test no 42                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.47
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.46
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.35
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.45
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.86
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.71
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.37
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.79
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.33
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6868.66
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.72
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.02
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.80
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.80
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.16
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908254
   j =  2                              :            45864
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
 p-value of test no 79                 :    0.9927
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
 p-value of test no 94                 :    0.9985
 
 Anderson-Darling statistic = A2       :    4.89
 p-value of test no 95                 :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9992    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.30
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.05
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.15
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.01
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.22
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.77
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.70
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17588.55
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.20
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.13
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.98
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.51
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.29
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.54
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.32
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.10
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.29
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.53
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.43
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.86
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   44.26
 p-value of test no 160                :    0.9976
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.73
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.72
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.75
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.05
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.51
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.40
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.91
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.42
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.15
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.92
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.23
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.51
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.17
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.14
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.90
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.62
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
 p-value of test no 190                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.10
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.38
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 204                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 205                :  6.4e-3
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 206                :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  262.55
 p-value of test no 207                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10129.68
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10253.58
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.60
 p-value of test no 217                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.01e-4
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.04
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.13
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.10
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.91
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11620.64
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.26
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.03
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000154072
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.64
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000012160
 
 Normal statistic for number of bits   :   0.096
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:05.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35523
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 4                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.99
 p-value of test no 47                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.49
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.34
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.03
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.74
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.78
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.37
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.85
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.76
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.61
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.28
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 62                 :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   93.90
 p-value of test no 65                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.07
 p-value of test no 66                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.70
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5131.46
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45745
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869745
   j =  1                              :        399908514
   j =  2                              :            45737
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46127
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870127
   j =  1                              :        399907748
   j =  2                              :            46123
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.29
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.47
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.84
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.26
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.53
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.03
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.97
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.16
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.14
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.57
 p-value of test no 135                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.84
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.16
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.86
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.43
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.90
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.93
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.20
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.87
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.68
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.39
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.01
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.37
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.13
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.25
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.70
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.06
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.95
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.03
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.01
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.83
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.84
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.58
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.79
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.12
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.22
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.48
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.95
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.94
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.43
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.05
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.27
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.49
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.87
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.99
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.83
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.14
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.17
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.09
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.35
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.56e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5082.88
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.51
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4056.89
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.78
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.18
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11578.51
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.07
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000008677
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.98
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000087745
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 238                :    0.66
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.032
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:53.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35524
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 8                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5319
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.97
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.14
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.14
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.08
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.19
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.52
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6988.26
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.80
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.15
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.92
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.34
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.61
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45856
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869856
   j =  1                              :        399908293
   j =  2                              :            45846
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908420
   j =  2                              :            45787
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.69e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.98
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.46
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.19
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.71
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.28
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.27
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.26
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.09
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.75
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.01
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.61
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 142                :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 144                :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16954.56
 p-value of test no 145                :    0.9949
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.68
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.68
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.20
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.99
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.96
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.44
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.13
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.02
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.60
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.21
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.11
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.82
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.48
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.77
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.67
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.54
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.62
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.47
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.37
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.42
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.15
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.15
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.26
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.74
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.81
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.70
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.61
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.65
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.60
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.70
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.66
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.57
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.08
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.42
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.43
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.21
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.76
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.75
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.84
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.27
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.19
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.30
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999890426
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.50
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999823442
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.46
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 243                :    0.51
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:48.28
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35525
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1532
 p-value of test no 11                 :  4.4e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334652
   j =  1                              :        599996936
   j =  2                              :             1532
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     554
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.31
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.95
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.90
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.62
 p-value of test no 51                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.68
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.18
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.41
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.67
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.13
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.06
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.82
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.03
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.22
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  165.29
 p-value of test no 67                 :  3.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4694.77
 p-value of test no 68                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46058
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870058
   j =  1                              :        399907887
   j =  2                              :            46052
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908056
   j =  2                              :            45960
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
 p-value of test no 93                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  5.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.89
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.80
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.96
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.39
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.72
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.90
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.21
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 127                :    0.9902
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.26
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.49
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.11
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.28
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.26
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17388.69
 p-value of test no 145                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.04
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.50
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.52
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.11
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.66
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.60
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.99
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.75
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.33
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.44
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.92
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.72
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.28
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.63
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.10
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.06
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.35
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.50
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.29
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.02
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.58
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.31
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.84
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.75
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.96
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.51
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.28
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.65
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.85
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.74
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9814.54
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 216                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.52
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.98
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4331.05
 p-value of test no 227                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.55
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.83
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.71
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.03
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999956207
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.55
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000067420
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.77
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:46.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           4.4e-6
  42  Permutation, t = 7              0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35526
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7465
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.59
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.73
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.27
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.30
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.03
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.55
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.95
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.30
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.49
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7073.36
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.61
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.46
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.26
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.02
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46186
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870186
   j =  1                              :        399907630
   j =  2                              :            46182
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908115
   j =  2                              :            45938
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 107                :    0.9921
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.89
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.77
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.47
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.42
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.76
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.76
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.32
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.12
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 134                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.49
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17237.79
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.55
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.98
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.69
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.62
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.15
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.68
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.02
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.75
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.45
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.86
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.19
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.08
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.45
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.41
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.27
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.11
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.64
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5394.24
 p-value of test no 168                :  5.9e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.98
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.75
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.74
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.23
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.03
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.77
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.81
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.07
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    2.01
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.34
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.76
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9918
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.39
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.23
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.32
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 219                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.40
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.53
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.05
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.90
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.86
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.83
 p-value of test no 230                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.22
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000022147
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.65
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999932198
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.59
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 253                :    0.12
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 J (L=10000, r=0)    5.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35527
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4454
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7433
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.11
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.36
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.54
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.36
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.75
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.23
 p-value of test no 53                 :  5.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.02
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.56
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.86
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.77
 p-value of test no 57                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.37
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.03
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.35
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.25
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5183.05
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908175
   j =  2                              :            45908
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908024
   j =  2                              :            45982
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9901
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.19
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.63
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.10
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.61
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.58
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.07
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.19
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.88
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.78
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.68
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.08
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.33
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.80
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.05
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.93
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.81
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.36
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.86
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.03
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.12
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.02
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.97
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.39
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.40
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.00
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.46
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.76
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.88
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.62
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.11
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.58
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.32
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.63
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.15
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.70
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.78
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.41
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.29
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.19
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.59
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.38
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10315.00
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.13
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4712.35
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4968.03
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.62
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.02
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.28
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.69
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.03
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000038662
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.06
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000129958
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 234                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    2.36
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.14
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35528
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 36                 :    0.9988
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.57
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.43
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.66
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.74
 p-value of test no 51                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.27
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.25
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.93
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.08
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.19
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7332.42
 p-value of test no 57                 :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.74
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.14
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.44
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.15
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.65
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908322
   j =  2                              :            45833
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.12
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.09
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.22
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.62
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.26
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.53
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.68
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.79
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.78
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.68
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17609.56
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.82
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.43
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.18
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.48
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.81
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.73
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.84
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.53
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.26
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.16
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.51
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.91
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.77
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.15
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.89
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.04
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.82
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.33
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.55
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.66
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.43
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.63
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.15
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.59
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.83
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.48
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.79
 p-value of test no 176                :  8.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.61
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.39
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.88
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.52
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 212                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9836.71
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.041
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4758.46
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.26
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3944.00
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.45
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11547.54
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.92
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.54
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000084928
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.60
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999905168
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.085
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35529
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5456
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.41
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.80
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.68
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.28
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.44
 p-value of test no 50                 :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.37
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.85
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.00
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.83
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.17
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.81
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.41
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.82
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.30
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.79
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909102
   j =  2                              :            45446
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46166
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870166
   j =  1                              :        399907672
   j =  2                              :            46158
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
 p-value of test no 79                 :    0.9950
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 91                 :  5.6e-3
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.14
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.67
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.24
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.83
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.44
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.98
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.67
 p-value of test no 133                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.35
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17200.41
 p-value of test no 145                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.71
 p-value of test no 146                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.73
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.16
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.90
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.03
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.01
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.04
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.73
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.71
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.36
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.32
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.95
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.91
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.20
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.54
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.39
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.90
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.79
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.94
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.90
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  317.20
 p-value of test no 166                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.28
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.54
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.27
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.22
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.19
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.69
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.18
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.82
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.08
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.43
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.77
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.87
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.24
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.62
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10076.55
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.033
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.23
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4867.33
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.53
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.15
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12303.60
 p-value of test no 229                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11523.54
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.39
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000103177
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.25
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999921074
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.031
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.71
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.78
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35530
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.12
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.03
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.45
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.75
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.39
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.28
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.06
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.29
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.60
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.40
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.99
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.38
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.21
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45794
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869794
   j =  1                              :        399908417
   j =  2                              :            45784
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908433
   j =  2                              :            45776
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.77
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.91
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.74
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.40
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.24
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.52
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.12
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.83
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.54
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.09
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17173.67
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.09
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.72
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.31
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.45
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.74
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.42
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.03
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.64
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.93
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.69
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.71
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.58
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.19
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.10
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.55
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.30
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.11
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.97
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.32
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.35
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.89
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.55
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.48
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.61
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.10
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.17
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.64
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.26
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.90
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.49
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.45
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.38
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.15
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.94
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4043.61
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.59
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.01
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.63
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000044185
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.43
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999986840
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.025
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    2.19
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:39.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35531
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7098
 p-value of test no 19                 :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.66
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     867
 p-value of test no 25                 :    0.86
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.60
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.99
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.05
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.08
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.85
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.15
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.23
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.31
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.12
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.74
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.12
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.23
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.42
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.68
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.13
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.66
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907805
   j =  2                              :            46084
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908131
   j =  2                              :            45927
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 110                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.61
 p-value of test no 117                :    0.9955
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.63
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.73
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.55
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.41
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.96
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.90
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.01
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.10
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.08
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.84
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17349.71
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.77
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.65
 p-value of test no 147                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.77
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.77
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.33
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.19
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.24
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.72
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.51
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.58
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.72
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.08
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.57
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.41
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.95
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.70
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.53
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.63
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.53
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.66
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.12
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.15
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.37
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.00
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.37
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.00
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4888.47
 p-value of test no 173                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.83
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.39
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.75
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    5.61
 p-value of test no 187                :  1.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.05
 p-value of test no 188                :    0.9989
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.02
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.06
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 205                :    0.99
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.97
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10191.91
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10127.15
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.36
 p-value of test no 217                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.38
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4969.52
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.26
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.19
 p-value of test no 228                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.49
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.56
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.15
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999980417
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.23
 p-value of test no 233                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000047326
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.19
 p-value of test no 244                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.045
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 253                :    0.16
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:18.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35532
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.48
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    3.39
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    4.76
 p-value of test no 44                 :  3.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.73
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.17
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.59
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.13
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.92
 p-value of test no 50                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.08
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.08
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.79
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.61
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1559.66
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6788.00
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.23
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.74
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.36
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.55
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5121.10
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907980
   j =  2                              :            46004
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908576
   j =  2                              :            45709
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.93
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.14
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.49
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.48
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.17
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.73
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.23
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.27
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.21
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.43
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17269.63
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.58
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.69
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.42
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.65
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.07
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.48
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.41
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.21
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.56
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.68
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.35
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.04
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.04
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.35
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.57
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.00
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.02
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.50
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.29
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.24
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.78
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5118.99
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.07
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.23
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.97
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.70
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.50
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.63
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.44
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.84
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.23
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.43
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.55
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.60
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.80
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9705.82
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.79
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.93
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.71
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.11
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.89
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11804.56
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.82
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000094315
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.09
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000034513
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.87
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:22.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35533
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 10                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.70
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.44
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.61
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.77
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.07
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.68
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.56
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.62
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.14
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.19
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.23
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.38
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.78
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5235.03
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45807
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869807
   j =  1                              :        399908389
   j =  2                              :            45801
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 81                 :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 106                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.33
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.99
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.68
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.18
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.72
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.10
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17535.19
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.75
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.70
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.27
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.80
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.51
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.57
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.72
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.66
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.56
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.83
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.26
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.83
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.62
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.20
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.06
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  556.70
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.16
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.71
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.07
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.63
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5130.91
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.90
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.19
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.85
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.23
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.90
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.50
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.73
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.81
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.20
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.79
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.099
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 3.86e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.073
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4695.64
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.80
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.72
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.00
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.96
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.89
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999811229
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.38
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000134527
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -8.14e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.74
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35534
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 3                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.93
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.60
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.30
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.70
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.98
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.67
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.48
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.80
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.45
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.16
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.84
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1558.64
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.69
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.07
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.39
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.81
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.86
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908353
   j =  2                              :            45807
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908532
   j =  2                              :            45734
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 76                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.05
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.02
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.36
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.54
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.23
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.60
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.70
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.39
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.37
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.38
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17546.55
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.92
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.68
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.78
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.88
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.98
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.79
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.98
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.29
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.73
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.50
 p-value of test no 155                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.68
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.62
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.30
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.83
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.04
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.05
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.76
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.57
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.39
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.11
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.22
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.49
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.09
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.17
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.14
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.16
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.19
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.88
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.37
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.03
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.79
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.33
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.24
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.34
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.49
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 208                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
 p-value of test no 209                :    0.9912
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9734.10
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10054.85
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.096
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.59
 p-value of test no 218                :  4.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.18
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.76
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.83
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4362.58
 p-value of test no 228                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.21
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.74
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.30
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999974987
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.75
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999986594
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 236                :  8.2e-4    *****
 
 Anderson-Darling statistic = A2       :    3.51
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.83
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35535
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.29
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.75
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.24
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.16
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.69
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.54
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.90
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.09
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.02
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.11
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.71
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6803.26
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.05
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.27
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.29
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.28
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.60
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46210
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870210
   j =  1                              :        399907580
   j =  2                              :            46210
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908684
   j =  2                              :            45652
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 97                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.58
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.83
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.03
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.54
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.78
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.38
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.66
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.14
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.27
 p-value of test no 136                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.73
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17670.86
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.06
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.62
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.53
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.75
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.00
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.48
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.25
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.23
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.92
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.78
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.77
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.20
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.55
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.84
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.66
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.57
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.87
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.11
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.83
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.95
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.03
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.74
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5181.34
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.36
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.10
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.47
 p-value of test no 171                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.49
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.44
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.50
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.50
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.90
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.41
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.56
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.12
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.26
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.44
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.85
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10193.24
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.78
 p-value of test no 216                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.59
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 223                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4991.43
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3940.18
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.91
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.11
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.19
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.64
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000061192
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.55
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999832496
 
 Normal statistic for number of bits   :   -1.32
 p-value of test no 234                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
 p-value of test no 251                :    0.9982
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:23.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35536
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.16
 p-value of test no 46                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.93
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.45
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.06
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.31
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.54
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.58
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.62
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.11
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7258.52
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.80
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.26
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.69
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.33
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5170.41
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908633
   j =  2                              :            45679
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908089
   j =  2                              :            45951
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.65
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.05
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.95
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.47
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.32
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.50
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.07
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17122.73
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.19
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.42
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.20
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.00
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.16
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.62
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.00
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.63
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.34
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.61
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.01
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.40
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  102.75
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.81
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.51
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.20
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.36
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.27
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.43
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.66
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5120.45
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.99
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.87
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.55
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.51
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.40
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.52
 p-value of test no 174                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.58
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.01
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.93
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.53
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.33
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.22
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.44
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10187.11
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.64
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.52
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.81
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3857.64
 p-value of test no 227                :    0.9982
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.19
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.15
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.23
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.76
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999969221
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.21
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999915317
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:50.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35537
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.14
 p-value of test no 28                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.77
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.08
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.11
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.79
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.68
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.70
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.08
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.71
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.65
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.56
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.72
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.39
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.86
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.56
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45847
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869847
   j =  1                              :        399908307
   j =  2                              :            45845
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908212
   j =  2                              :            45888
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 73                 :  4.6e-3
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.90
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.15
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.24
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.30
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.80
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.38
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.81
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.65
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.70
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.19
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17858.11
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.31
 p-value of test no 147                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.84
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.32
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.74
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   16.16
 p-value of test no 151                :    0.9982
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.20
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.23
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.56
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.61
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.30
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.80
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.97
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.23
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.02
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.49
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.24
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.77
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.91
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.49
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.20
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4852.37
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.62
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.06
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.67
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.85
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.51
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.90
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.93
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.59
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.96
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.022
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.23
 p-value of test no 189                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.51
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.87
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10174.62
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10196.18
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.79
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.63
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4245.99
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.37
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11812.50
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.63
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.72
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000229456
 
 Normal statistic for number of bits   :    1.81
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.02
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000170146
 
 Normal statistic for number of bits   :    1.35
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:02.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35538
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7502
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7069
 p-value of test no 21                 :    0.9983
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.18
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.28
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.63
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.55
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.12
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.81
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.39
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7175.82
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.73
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.46
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.27
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.09
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.33
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908565
   j =  2                              :            45710
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908209
   j =  2                              :            45888
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.88
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.33
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.97
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.21
 p-value of test no 122                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.96
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.44
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.46
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.72
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.95
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.74
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.02
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.72
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17566.06
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   77.16
 p-value of test no 146                :  8.0e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.38
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.83
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.65
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.40
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.28
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.69
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.20
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  200.69
 p-value of test no 156                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.77
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.22
 p-value of test no 158                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.03
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.86
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.98
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.78
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.83
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.62
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.68
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.12
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.88
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.12
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.77
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.65
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.66
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.90
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.33
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.40
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.63
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.03
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.69
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.74
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 183                :    0.04
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    2.04
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.37
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.05
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.38
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.86
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.20
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.58
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.099
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.48
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.03
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.63
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.90
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.64
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.50
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.05
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999978938
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.68
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000044794
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.088
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:20.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       8.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35539
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4462
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 45                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.88
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.84
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.95
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.42
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.18
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.50
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.66
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.82
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.21
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.72
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.95
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.69
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.82
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.69
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.52
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5047.08
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908520
   j =  2                              :            45737
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45992
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869992
   j =  1                              :        399908022
   j =  2                              :            45980
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 87                 :  2.6e-3
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.14
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.24
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.26
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.12
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.11
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.52
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.72
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.40
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.23
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.42
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17152.58
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.80
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.48
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.95
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.39
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.57
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.19
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.67
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.86
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.12
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.10
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.86
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.94
 p-value of test no 160                :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.89
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.75
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.56
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.48
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.71
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.44
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.37
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.51
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.05
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.07
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.02
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.01
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.23
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.43
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.75
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.54
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.10
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.57
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 209                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.42
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.46
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.19
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.95
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.88
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.88
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.40
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.98
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.66
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999970895
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.89
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000051853
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 242                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 246                :  1.8e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 253                :    0.09
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:30.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35540
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5530
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 16                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 24                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.48
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.55
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    4.22
 p-value of test no 38                 :  6.8e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    3.40
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.89
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.49
 p-value of test no 49                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.04
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.15
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.41
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  176.76
 p-value of test no 54                 :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.71
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.31
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.32
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.65
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.27
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.83
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.91
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.55
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907690
   j =  2                              :            46152
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908359
   j =  2                              :            45810
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    3.39
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.20
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.47
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.44
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.08
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.85
 p-value of test no 123                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.59
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.32
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.97
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.75
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.72
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17211.42
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.98
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.41
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.53
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.64
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.67
 p-value of test no 150                :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.78
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.86
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.34
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.73
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.91
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.07
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.39
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.90
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.79
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.03
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.73
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.35
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.22
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.72
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.38
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.36
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.36
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.12
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.40
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.07
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.17
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.14
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.71
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.06
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.96
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.51
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.43
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.07
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.65
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.32
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.29
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.07
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4286.68
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.93
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.94
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.65
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.55
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000035209
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.86
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999878771
 
 Normal statistic for number of bits   :   -0.96
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:53.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35541
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 20                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.08
 p-value of test no 35                 :  8.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.77
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.08
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.15
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.85
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.54
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.68
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.37
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.63
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.32
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.31
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.45
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.62
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.11
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.19
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.47
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.32
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.30
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908235
   j =  2                              :            45881
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908474
   j =  2                              :            45763
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.43
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.86
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.30
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.37
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.94
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.19
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
 p-value of test no 127                :    0.9962
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.08
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.93
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.91
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.65
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.43
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17363.69
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.32
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.64
 p-value of test no 147                :  2.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.33
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.80
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.73
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.98
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.30
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.13
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.19
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.18
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.28
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.33
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.43
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.84
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.74
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.10
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  481.01
 p-value of test no 166                :  5.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.65
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.54
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.45
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.41
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.58
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.89
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.89
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.77
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.43
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.16
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.34
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.68
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    1.97
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.68
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.63
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.43
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10289.94
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.45
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.06
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.52
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.74
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.51
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.60
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11564.02
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.87
 p-value of test no 231                :    0.9969
 
 
 -----------------------------------------------
 Total number of bits:  7999921443
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.00
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999978635
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:05.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 H (L=10000, r=0)    5.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35542
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 8                  :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5351
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7552
 p-value of test no 18                 :  3.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    4.52
 p-value of test no 45                 :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.58
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.94
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.38
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.99
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.77
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.23
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.14
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.88
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.75
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7040.36
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.45
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.58
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.48
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.42
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.68
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908099
   j =  2                              :            45949
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907704
   j =  2                              :            46136
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 99                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.75e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.87
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.21
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.32
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.71
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.51
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.16
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.27
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.40
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.41
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.90
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.02
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.25
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.15
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.00
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.61
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.89
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.49
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.82
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.74
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.11
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.28
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.90
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.34
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.55
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.09
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.84
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.66
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.86
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.59
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.30
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.62
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4909.04
 p-value of test no 168                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.02
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.90
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.14
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.24
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.14
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.37
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.47
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.49
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.48
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.83
 p-value of test no 179                :    0.9977
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.62
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.43
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.93
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.41
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.39
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.82
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.78
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.86
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4417.54
 p-value of test no 227                :  5.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.83
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.10
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12121.01
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.60
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999960599
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.54
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999989816
 
 Normal statistic for number of bits   :  -0.081
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:51.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  97  HammingIndep, L=300, r=0        5.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35543
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7519
 p-value of test no 21                 :  9.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.93
 p-value of test no 22                 :  9.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.48
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.72
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.44
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.90
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.75
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.16
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.52
 p-value of test no 54                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.58
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1541.40
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.78
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.17
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.75
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.05
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.48
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.34
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908318
   j =  2                              :            45841
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907877
   j =  2                              :            46057
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-3
 p-value of test no 76                 :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.79
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.12
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.25
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.97
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.95
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.20
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 130                :  3.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.46
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.91
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.18
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.11
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.56
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.65
 p-value of test no 148                :    0.9945
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.35
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.66
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.61
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.77
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.49
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.59
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.75
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.47
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.64
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.21
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.89
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.24
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.21
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.58
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.26
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.97
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.00
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.32
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.63
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.32
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  450.84
 p-value of test no 172                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.12
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.74
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.98
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.99
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.37
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.78
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.23
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.17
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
 p-value of test no 209                :    0.9973
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9672.52
 p-value of test no 211                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.81
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.69
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.48
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.22
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.00
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11991.62
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.45
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.55
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000130477
 
 Normal statistic for number of bits   :    1.03
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.71
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999914285
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:14.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35544
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  4.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 36                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.22
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.75
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.51
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.46
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.39
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.65
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.38
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.61
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.28
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.36
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.51
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  156.38
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5011.50
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46011
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870011
   j =  1                              :        399907981
   j =  2                              :            46005
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908560
   j =  2                              :            45717
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    4.82
 p-value of test no 74                 :  3.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  1.8e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.46
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.69
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.07
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.07
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.05
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.20
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.77
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.92
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.73
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17562.86
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.99
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.86
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.75
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.85
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.16
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.82
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.63
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.77
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.55
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.59
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.76
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.46
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.46
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.43
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.81
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.26
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.92
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.07
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.87
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.00
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.86
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.27
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.38
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.96
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.83
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.10
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.27
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.44
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.19
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.70
 p-value of test no 176                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.91
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.20
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.79
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.31
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10169.40
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.35
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.09
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.70
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.90
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.77
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.06
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.38
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999978407
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.41
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999772922
 
 Normal statistic for number of bits   :   -1.80
 p-value of test no 234                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 238                :    0.88
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 247                :    0.9990
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35545
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.27
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.11
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.22
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.46
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.69
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.55
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.14
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.18
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7159.46
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.99
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.35
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.52
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.46
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.56
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45529
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869529
   j =  1                              :        399908945
   j =  2                              :            45523
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908528
   j =  2                              :            45730
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.90
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.74
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.73
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.85
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.88
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.79
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.83
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.08
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.24
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.29
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17666.61
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.92
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.61
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.01
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.33
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.14
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.09
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.29
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.29
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.89
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.41
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.52
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.34
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.16
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.01
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.62
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.82
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.71
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.78
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.30
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.70
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.96
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.75
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.63
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.65
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.19
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.34
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.87
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.39
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.73
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.91
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.39
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.32
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.94
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.22
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.50
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.66
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.34
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.93
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.26
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12170.81
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.03
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.97
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000065551
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.00
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000061261
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.18
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 248                :    0.32
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:59.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35546
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 4                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997197
   j =  2                              :             1400
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1484
 p-value of test no 12                 :  7.2e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334604
   j =  1                              :        599997032
   j =  2                              :             1484
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    3.20
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.59
 p-value of test no 38                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.73
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.31
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.48
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.88
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.26
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.52
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.44
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.07
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.39
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.16
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.02
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9964
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.79
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.47
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.71
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.93
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.72
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908217
   j =  2                              :            45884
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908782
   j =  2                              :            45603
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.43e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.28
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.49
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.39
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.92
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.93
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.77
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.92
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17211.26
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.50
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.08
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.68
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.12
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.40
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.24
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.02
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.02
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.45
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.79
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.62
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.97
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.20
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.13
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.50
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.29
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.45
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.83
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.84
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.03
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.98
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.50
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.69
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.61
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.41
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.50
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.83
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 180                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.42
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.37
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.91
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 200                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 202                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.17
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.95
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.93
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.22
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 219                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4713.48
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.74
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.92
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.03
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.84
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.69
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.61
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999915719
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.64
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999993350
 
 Normal statistic for number of bits   :  -0.053
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:43.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35547
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.55
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.12
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.42
 p-value of test no 51                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.40
 p-value of test no 52                 :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.09
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.65
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.17
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.40
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6856.76
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.46
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 62                 :  3.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.23
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.22
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.82
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.61
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908498
   j =  2                              :            45751
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908077
   j =  2                              :            45957
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 85                 :  6.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.79
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.73
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.75
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.02
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.74
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.05
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.87
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.47
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.36
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.13
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.91
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.74
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.21
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.76
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.53
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.24
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.80
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.18
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.25
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.29
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.48
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.72
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.69
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.20
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.72
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.65
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.23
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.94
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.28
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.35
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.15
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.46
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.14
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.38
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.35
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.31
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.68
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.64
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.69
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.07
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.04
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.45
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10014.97
 p-value of test no 211                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10214.74
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.75
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.18
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.14
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.15
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.64
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.14
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.43
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999999554
 
 Normal statistic for number of bits   : -3.53e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.92
 p-value of test no 233                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  7999969839
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.047
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.18
 p-value of test no 244                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:47.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35548
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.26
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 41                 :    0.9914
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.89
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.49
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.79
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.04
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.15
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.19
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6858.80
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.38
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 64                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.67
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.46
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.15
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.32
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46090
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870090
   j =  1                              :        399907822
   j =  2                              :            46086
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46051
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870051
   j =  1                              :        399907901
   j =  2                              :            46045
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.15
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.04
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.65
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.59
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.10
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.73
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 127                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.84
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.02
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.94
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17432.98
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.14
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.08
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.65
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.54
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.13
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.49
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.16
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.73
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.27
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.09
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.74
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.77
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.62
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.85
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.10
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.13
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.22
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.03
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.58
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  478.53
 p-value of test no 169                :  3.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.85
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.86
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.42
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.98
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.72
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.84
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.36
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.89
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.34
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.26
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 187                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.37
 p-value of test no 188                :  8.9e-3
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.63
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 200                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.64
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-4
 p-value of test no 205                :    0.9992    *****
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.26
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.47
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.71
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 218                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.79
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.79
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.37
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.42
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11510.90
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.30
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.99
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000093916
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.67
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000034039
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.46
 
 Sample variance                       :    1.52
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:44.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)    3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35549
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    2.70
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.96
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.53
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.12
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.08
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.83
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.50
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.68
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.36
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.13
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.20
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.88
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.70
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.94
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.64
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5167.00
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908495
   j =  2                              :            45751
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45531
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869531
   j =  1                              :        399908939
   j =  2                              :            45529
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 104                :  5.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 105                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.01
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.81
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.66
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.84
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.98
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.70
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.07
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.99
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.94
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.35
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.75
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.39
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.14
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.30
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.21
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.02
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.10
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.81
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.23
 p-value of test no 157                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.15
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  183.54
 p-value of test no 159                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.57
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.41
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.40
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.61
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.84
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.61
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  308.89
 p-value of test no 166                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.89
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5013.98
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.05
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.35
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  453.34
 p-value of test no 172                :  8.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.04
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.37
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.69
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.71
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.28
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.15
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 188                :    0.53
 
 Sample variance                       :    0.68
 p-value of test no 189                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.83
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.47
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.07
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.21
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.44
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5009.50
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.59
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.04
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.97
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11590.09
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.05
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.56
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999991013
 
 Normal statistic for number of bits   :  -0.071
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.90
 p-value of test no 233                :  6.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000030607
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.71
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:39.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35550
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9914
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 5                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 11                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5291
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4203
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    2.69
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.94
 p-value of test no 29                 :  3.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.83
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.50
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.63
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.08
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.36
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.23
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.49
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.96
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.64
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.65
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6928.96
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.97
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 62                 :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.80
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.77
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.25
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908520
   j =  2                              :            45734
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45711
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869711
   j =  1                              :        399908581
   j =  2                              :            45705
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 78                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.46e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.71
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.60
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.06
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.05
 p-value of test no 122                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.51
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.86
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.86
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.71
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17681.96
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.63
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.38
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.84
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.34
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.79
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.89
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.66
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.50
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.64
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.68
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.27
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.44
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.50
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.79
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.96
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.51
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.27
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.62
 p-value of test no 166                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.92
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5273.88
 p-value of test no 168                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.17
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.79
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.58
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.35
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.39
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.06
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.33
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.26
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.68
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 185                :    0.9960
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 186                :    0.01
 
 Anderson-Darling statistic = A2       :    4.95
 p-value of test no 187                :  3.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.23
 p-value of test no 188                :  6.1e-4    *****
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.56
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.68
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.32
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.98
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.30
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.012
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.83
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.34
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.28
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.98
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.55
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.29
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.23
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000016372
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.92
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000092701
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.64
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                0.9999 
  83  LempelZiv, r = 15               6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35551
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1470
 p-value of test no 6                  :  2.4e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334590
   j =  1                              :        599997060
   j =  2                              :             1470
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4219
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.49
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.68
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.00
 p-value of test no 47                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.62
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.74
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.31
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.04
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.16
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.97
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.94
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.59
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.93
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.44
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.38
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  141.73
 p-value of test no 67                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.59
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908127
   j =  2                              :            45932
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45927
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869927
   j =  1                              :        399908149
   j =  2                              :            45921
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 74                 :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9936
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 111                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.071
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.43
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.17
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.57
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.20
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.86
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.69
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.32
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.34
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.40
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.87
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.60
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.87
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.32
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.48
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.52
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.81
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.59
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.29
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.76
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.24
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.73
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.25
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.30
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.02
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.00
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.50
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.77
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.65
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.44
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.02
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.90
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.40
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.39
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.50
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.79
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.73
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.68
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.31
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.41
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.70
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.33
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.30
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.19
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.32
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.94
 p-value of test no 203                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.50
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9877.97
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.20
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.76
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.26
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.03
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.52
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.37
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.62
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.20
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000140506
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.70
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999757730
 
 Normal statistic for number of bits   :   -1.92
 p-value of test no 234                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:29.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35552
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997273
   j =  2                              :             1362
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    4.43
 p-value of test no 39                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.79
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.46
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.20
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.73
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.47
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.54
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.53
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.16
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.91
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.82
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.64
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.60
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.20
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.76
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.45
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907748
   j =  2                              :            46114
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908274
   j =  2                              :            45851
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
 p-value of test no 84                 :    0.9969
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.84
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.91
 p-value of test no 120                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.87
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.87
 p-value of test no 122                :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.51
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.50
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.52
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.41
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.46
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.73
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 139                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  164.39
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17561.78
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.13
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.67
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.30
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.20
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.31
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.03
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.57
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.66
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.41
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.36
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.55
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.08
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.53
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.79
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.73
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.70
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.00
 p-value of test no 166                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.65
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.88
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.94
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.79
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.49
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.40
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.47
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.38
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.22
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.79
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.09
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.96
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.72
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.60
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.20
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.85
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9835.73
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.27
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.21
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5018.95
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.81
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.33
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11624.53
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.31
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   97.39
 p-value of test no 231                :  2.7e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999935174
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.80
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000027571
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 242                :    0.9953
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.042
 p-value of test no 243                :    0.52
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  101  Run of bits, r = 0              2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35553
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 11                 :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5540
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7067
 p-value of test no 21                 :    0.9984
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.47
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    2.75
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.39
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.66
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.72
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.39
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.73
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.27
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.53
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.45
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.38
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7223.81
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.86
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.89
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.61
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.64
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.45
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907991
   j =  2                              :            45997
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908350
   j =  2                              :            45822
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 94                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 102                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
 p-value of test no 112                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.81
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.47
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.84
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.70
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.29
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.12
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.23
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.54
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.03
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17746.49
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.23
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.23
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.06
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.67
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.32
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.91
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.26
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.62
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.13
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.38
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.41
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.77
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.59
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.54
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.11
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.01
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.46
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.38
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.05
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.87
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.31
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.41
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.73
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.00
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4738.24
 p-value of test no 173                :    0.9961
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.15
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.01
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.11
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.09
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.15
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.39
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 208                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10364.23
 p-value of test no 211                :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9977.03
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.73
 p-value of test no 217                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.99
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.58
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.13
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.76
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.51
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.91
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.41
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000109612
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.89
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000070903
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    2.26
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 242                :    0.9969
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35554
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4550
 p-value of test no 17                 :  6.7e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.88
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 38                 :    0.9972
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.21
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.85
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.20
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.56
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.41
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.06
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.14
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.63
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.71
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.81
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.77
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.04
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.39
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.30
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.71
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5210.38
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908783
   j =  2                              :            45601
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
 p-value of test no 97                 :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.55e-4
 p-value of test no 109                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.56
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.85
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.24
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.41
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.06
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.57
 p-value of test no 125                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.75
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.17
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.03
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.71
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.13
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.44
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17253.09
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.30
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.58
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.68
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.90
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.23
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.22
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.10
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.44
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.87
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   91.17
 p-value of test no 156                :    0.9999    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.60
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.96
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.64
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.01
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.50
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.88
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.39
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.68
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.17
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.59
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.72
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.24
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.59
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.82
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.99
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.60
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.06
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.30
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.53
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.47
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.87
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.86
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.59
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.90
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.25
 p-value of test no 215                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.10
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.87
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.52
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.46
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.98
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.56
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.91
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999993671
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.09
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999940223
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:58.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         6.7e-4
  76  RandomWalk1 H (L=1000, r=0)     0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35555
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 4                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5659
 p-value of test no 13                 :  6.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4205
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4485
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.93
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.38
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.84
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.09
 p-value of test no 50                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.86
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.17
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.32
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.62
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.87
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.46
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.64
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.88
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.35
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.36
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4852.65
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908282
   j =  2                              :            45853
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908331
   j =  2                              :            45824
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 95                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.93
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.18
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.37
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.86
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.61
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   79.76
 p-value of test no 124                :  5.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.06
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.59
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.59
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.44
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.55
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17233.13
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.56
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.87
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.58
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.32
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.51
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.51
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.01
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.65
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.30
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.27
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.68
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.37
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.49
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.89
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.80
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.47
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.31
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.83
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.63
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.29
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.99
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.83
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.60
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.42
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.28
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.69
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.50
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.36
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.75
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.44
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 183                :    0.33
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 187                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.76
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  247.19
 p-value of test no 203                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.57
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.04
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10124.73
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.17
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.61
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.41
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.91
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.88
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.63
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.60
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999905570
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.41
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000039877
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.013
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  13  BirthdaySpacings, t = 2         6.8e-4
  64  WeightDistrib, r = 26           5.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35556
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4465
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.20
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.19
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.78
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.11
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.25
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.03
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.48
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.41
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.76
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7189.82
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.94
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.08
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.78
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4895.33
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45842
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869842
   j =  1                              :        399908319
   j =  2                              :            45836
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45925
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869925
   j =  1                              :        399908153
   j =  2                              :            45919
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.72
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.32
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.24
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.12
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.30
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.49
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.43
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.42
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.76
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.37
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.39
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.39
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.80
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.54
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.89
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.10
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.07
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.56
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.89
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.09
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.48
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.61
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.16
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.46
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.58
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.96
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.51
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.90
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5210.84
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  446.69
 p-value of test no 169                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.66
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.09
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.82
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.78
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.87
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.23
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.52
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.31
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.86
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.63
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.94
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.44
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.36
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.76
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.82
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.71
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.58
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.63
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.90
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.11
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.51
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.77
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11818.67
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.19
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.09
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000002293
 
 Normal statistic for number of bits   :   0.018
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.42
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000094726
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 248                :    0.94
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:22.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35557
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5560
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.38
 p-value of test no 29                 :  5.9e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.81
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    4.89
 p-value of test no 38                 :  3.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    2.47
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.22
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.02
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.69
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.05
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.78
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.34
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.81
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.48
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.54
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.82
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.26
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.93
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.39
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.28
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.31
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.86
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45609
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869609
   j =  1                              :        399908784
   j =  2                              :            45605
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908676
   j =  2                              :            45659
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.18e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.97
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.01
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.62
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.71
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.57
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.55
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.35
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.82
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.57
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.26
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.65
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.84
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.17
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.69
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.55
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.86
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.30
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.83
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.69
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.95
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.31
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.00
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.22
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.38
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.95
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.10
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.94
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.50
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.90
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.00
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.98
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.55
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.92
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.72
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.49
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.13
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.20
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.68
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.22
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.41
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.50
 p-value of test no 179                :    0.9938
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.03
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.19
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.19
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.56
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.91
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.53
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4762.98
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.63
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.58
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.50
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.39
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.39
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.13
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000017005
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.17
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000054940
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.51
 p-value of test no 243                :    0.9940
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.49
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35558
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 10                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 11                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 18                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     595
 p-value of test no 31                 :    0.57
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 45                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.22
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.84
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.23
 p-value of test no 48                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.07
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.45
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.81
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.13
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.13
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.23
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7229.71
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.87
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.00
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.40
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.23
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.58
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908666
   j =  2                              :            45661
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46045
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870045
   j =  1                              :        399907912
   j =  2                              :            46041
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.96
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.30
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.32
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.45
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.21
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.69
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 126                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.02
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.34
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.55
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.29
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17345.44
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.47
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.28
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.47
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.31
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.55
 p-value of test no 152                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.99
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.99
 p-value of test no 154                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.29
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.52
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.38
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.81
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.60
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.86
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.96
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  544.27
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.56
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.75
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.54
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.20
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.14
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.17
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.12
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.03
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.93
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.30
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.76
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.33
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.64
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.73
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.18
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.95
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.21
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.86
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9880.42
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.49
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.64
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.09
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.10
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.72
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.33
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.84
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000105949
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.22
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000096130
 
 Normal statistic for number of bits   :    0.76
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    2.11
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35559
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7123
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.93
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.20
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.89
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.69
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.05
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.67
 p-value of test no 53                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.70
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.64
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.78
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7105.88
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.38
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.11
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.63
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.30
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5015.33
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908699
   j =  2                              :            45646
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46074
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870074
   j =  1                              :        399907858
   j =  2                              :            46062
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.08
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.64
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.20
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.37
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.60
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.38
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.00
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.58
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.36
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.15
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17289.32
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.67
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.49
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.69
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.64
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.82
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.63
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.25
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.32
 p-value of test no 155                :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.24
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.85
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.11
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.99
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.66
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.78
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.48
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.59
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.84
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.98
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.90
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.50
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.75
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.35
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.73
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.77
 p-value of test no 173                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.40
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.49
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.15
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 188                :  4.7e-3
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
 p-value of test no 190                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.32
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.27
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10100.46
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.75
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.11
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.83
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5097.07
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.73
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.47
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.26
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.97
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.65
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000158314
 
 Normal statistic for number of bits   :    1.25
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.43
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000055315
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 253                :    0.60
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:12.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35560
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5543
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.45
 p-value of test no 35                 :  5.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.96
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.55
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.32
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.17
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.73
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.81
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.03
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.74
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.84
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.28
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.64
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.45
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.66
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.35
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.83
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907921
   j =  2                              :            46038
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45644
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869644
   j =  1                              :        399908718
   j =  2                              :            45632
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.035
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.09
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.76
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.21
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.73
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.71
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.66
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.44
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.37
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.08
 p-value of test no 141                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17182.85
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.73
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.88
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.98
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.44
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.15
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.11
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.61
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.31
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.54
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.99
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.84
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.46
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.48
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.82
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.37
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.27
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.97
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.29
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.27
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.39
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.77
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.76
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.20
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.36
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.06
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.06
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.34
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.69
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.13
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.17
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.14
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.22
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.31
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.11
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.30
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.49
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.077
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.16
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.76
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.86
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.28
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11934.43
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12121.35
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.56
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000037021
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.40
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999991115
 
 Normal statistic for number of bits   :  -0.070
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:03.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35561
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7131
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.52
 p-value of test no 23                 :  5.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 40                 :    0.9948
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.92
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.16
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.89
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  290.86
 p-value of test no 54                 :  5.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.42
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.66
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6902.63
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.25
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.84
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.17
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.81
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907963
   j =  2                              :            46014
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908303
   j =  2                              :            45841
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.17
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.82
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.72
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.56
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.00
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.90
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.12
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.92
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.00
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17450.78
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.70
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.93
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.02
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.66
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.38
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   47.16
 p-value of test no 153                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.09
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.83
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.19
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.68
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.01
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.76
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.81
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.18
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.06
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.27
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.06
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.48
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.89
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.78
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.01
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.47
 p-value of test no 169                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.21
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.66
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.27
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.17
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.13
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.42
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.19
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.07
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.87
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 200                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 201                :    0.99
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.54
 p-value of test no 203                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.42
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.03
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.49
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.07
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.56
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.31
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.70
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.50
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.52
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.47
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000146776
 
 Normal statistic for number of bits   :    1.16
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.42
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999988691
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.46
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:51.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35562
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5601
 p-value of test no 13                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    2.17
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    3.94
 p-value of test no 45                 :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.41
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.51
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.18
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.59
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.52
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.06
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.30
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.55
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.09
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.81
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.53
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.33
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.73
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.80
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.69
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45412
 p-value of test no 70                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869412
   j =  1                              :        399909181
   j =  2                              :            45402
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908233
   j =  2                              :            45879
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9937
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 111                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.77
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.70
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.02
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.04
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.41
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.61
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.20
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.27
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.98
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.46
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  8.9e-3
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 144                :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17925.73
 p-value of test no 145                :  4.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.29
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.77
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.60
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.58
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.01
 p-value of test no 150                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.08
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.42
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.73
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.02
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.41
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.73
 p-value of test no 159                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.58
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.31
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.18
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.08
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.48
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.61
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.53
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.88
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.51
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.31
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.13
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.38
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.77
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.75
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.79
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.95
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.98
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.56
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.96
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.64
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.84
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
 p-value of test no 208                :    0.9973
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10263.64
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.79
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.77
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.49
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3927.04
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.62
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.20
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.81
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.80
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000083533
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.83
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000038782
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:36.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35563
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5549
 p-value of test no 13                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7481
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.71
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.90
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    3.47
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    4.43
 p-value of test no 44                 :  5.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.52
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.31
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.17
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.32
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.93
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.51
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.96
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.09
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.76
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.11
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.88
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.81
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.18
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.09
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4898.06
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908500
   j =  2                              :            45747
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908091
   j =  2                              :            45950
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 92                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 94                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.069
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.18
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.06
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.89
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.00
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.41
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.90
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.82
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.33
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9950
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.97
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.86
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.27
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.59
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.02
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.78
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.39
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.07
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.90
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.50
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.43
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.65
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.30
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.41
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.19
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.79
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.45
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.65
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.74
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.21
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.17
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.55
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.37
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.81
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.33
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.35
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.88
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.58
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.35
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.49
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.29
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.12
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.75
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.47
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.60
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.43
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.57
 p-value of test no 179                :    0.9949
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.02
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.95
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.33
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.89
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.96
 p-value of test no 217                :  1.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.22
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.27
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.56
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4202.11
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.50
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.42
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.09
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999984575
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.87
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999987356
 
 Normal statistic for number of bits   :  -0.100
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:01.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35564
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 32                 :    0.9942
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    3.72
 p-value of test no 45                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.56
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.87
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.79
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.91
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.86
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.70
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.68
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.95
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.91
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.67
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.46
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.99
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.66
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.89
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.38
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908149
   j =  2                              :            45924
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907936
   j =  2                              :            46029
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 101                :    0.95
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
 p-value of test no 103                :    0.9975
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.33
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.65
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.05
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.58
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.16
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.88
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.52
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.86
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.96
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.61
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.69
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.12
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.88
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.51
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.85
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.66
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.58
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.69
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.77
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.43
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.86
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.00
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.29
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.61
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.91
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.36
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.65
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.02
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.59
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.59
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.29
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.84
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.08
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.70
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.33
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.41
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.32
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.68
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.50
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.90
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.25
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.41
 p-value of test no 183                :  8.0e-3
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   24.01
 p-value of test no 196                :  2.3e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.28
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.28
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.73
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.35
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.9e-3
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10238.89
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.31
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.91
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.44
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.51
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.14
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.07
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.71
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999823589
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.47
 p-value of test no 233                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000037300
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.38
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.22
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:08.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35565
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1489
 p-value of test no 11                 :  4.5e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334609
   j =  1                              :        599997022
   j =  2                              :             1489
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.06
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.55
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.15
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.79
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.40
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  186.37
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.04
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1357.96
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.77
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
 p-value of test no 58                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.68
 p-value of test no 59                 :  4.2e-3
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 60                 :  2.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   61.64
 p-value of test no 61                 :  5.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.35
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.51
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.26
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908132
   j =  2                              :            45928
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908127
   j =  2                              :            45929
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 116                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.71
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.94
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.88
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.28
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.78
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 126                :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.80
 p-value of test no 129                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.84
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.071
 p-value of test no 134                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.77
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.21
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.82
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.64
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.25
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.90
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.91
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.46
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.86
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.34
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.16
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.72
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.24
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.09
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.16
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.13
 p-value of test no 161                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.58
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.02
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.33
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.06
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.98
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.11
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.75
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.39
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.72
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.28
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.22
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.35
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.37
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.98
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.21
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.43
 p-value of test no 179                :    0.9924
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.09e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.43
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.75
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.16
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.67
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.41
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.72
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.57
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.34
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.01
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.90
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.46
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000145867
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.00
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999972257
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:02.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           4.5e-4
  38  Run, r = 0                      5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35566
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 20                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.14
 p-value of test no 38                 :    0.9989
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.41
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.72
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.46
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.06
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.93
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.50
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  287.87
 p-value of test no 54                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.55
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.09
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.21
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.06
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.85
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.48
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.97
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.72
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908144
   j =  2                              :            45922
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907802
   j =  2                              :            46096
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
 p-value of test no 94                 :    0.9958
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.00
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.54
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.97
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.01
 p-value of test no 122                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.49
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.04
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.26
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.56
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.27
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.49
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17169.03
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.75
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.98
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.28
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.50
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.05
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.77
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.48
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.67
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.58
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.03
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.63
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.12
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.01
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.25
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.73
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.65
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.33
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.44
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.49
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.36
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.65
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.30
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  464.56
 p-value of test no 172                :  3.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.51
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.77
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.05
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.20
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.39
 p-value of test no 178                :  9.5e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.24
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 188                :    0.81
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.71
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.32
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.10
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.82
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.01
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.34
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.16
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.98
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.53
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.00
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.34
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.82
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.25
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999881546
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.00
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000029386
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:36.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35567
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 7                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997321
   j =  2                              :             1338
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 12                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     565
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 32                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.78
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.33
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.24
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.70
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.23
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.33
 p-value of test no 51                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.64
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.95
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.85
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.60
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6777.07
 p-value of test no 57                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.77
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.74
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.91
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.11
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4859.00
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907940
   j =  2                              :            46027
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908468
   j =  2                              :            45763
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 104                :    0.9940
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.30
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.80
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.12
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.78
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   62.32
 p-value of test no 123                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.89
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.02
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.76
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.97
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.49
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.61
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.87
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.77
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.81
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.66
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.55
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.31
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.95
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.22
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.67
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.32
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.71
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.08
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.66
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.82
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.32
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.47
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.49
 p-value of test no 165                :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.87
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.89
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.06
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.52
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.92
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.72
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.87
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4780.20
 p-value of test no 173                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.39
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  266.14
 p-value of test no 175                :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.13
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.70
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.30
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.00
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.26
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.79
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10121.45
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.60
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.38
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.30
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.37
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.53
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.65
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.34
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.95
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999971246
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.35
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000056890
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 248                :    0.97
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:09.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35568
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1499
 p-value of test no 5                  :  1.7e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334619
   j =  1                              :        599997002
   j =  2                              :             1499
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.20
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    3.26
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 35                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.55
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.28
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.10
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.22
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.01
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.91
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.35
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.91
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.98
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.90
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6929.23
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.67
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.35
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.73
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5156.15
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908481
   j =  2                              :            45758
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908381
   j =  2                              :            45805
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.33
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.54
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.30
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.93
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.84
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.42
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.87
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.01
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.16
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 139                :    0.01
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.14
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.01
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.16
 p-value of test no 146                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.03
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.32
 p-value of test no 148                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.41
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.96
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.67
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.56
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.65
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.10
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.66
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.38
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.02
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.71
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.99
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.59
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.05
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.57
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.33
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.99
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4841.74
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.47
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.68
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.66
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.70
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.79
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.58
 p-value of test no 174                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.52
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.92
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.69
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.90
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.70
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.15
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.88
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.87
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.78
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.02
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5068.56
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5055.59
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.64
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.90
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.11
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.43
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.86
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000040336
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.44
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000035032
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 246                :  1.1e-3
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 247                :  5.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.26
 p-value of test no 248                :    0.01
 
 Sample variance                       :    2.38
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:04.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   5  CollisionOver, t = 3            1.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35569
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5414
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    5.77
 p-value of test no 32                 :  1.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 40                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 46                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.97
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.70
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.50
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.05
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.00
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.26
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.31
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.34
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.59
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.33
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.40
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.19
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.54
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4856.33
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908594
   j =  2                              :            45697
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46356
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870356
   j =  1                              :        399907292
   j =  2                              :            46348
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
 p-value of test no 79                 :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 101                :    0.78
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.97
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.66
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.84
 p-value of test no 121                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.23
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.93
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.34
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.33
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.44
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.63
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.69
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.06
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.53
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.80
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.48
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.27
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.34
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.71
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.86
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.60
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.20
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.93
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.40
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.18
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 161                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.33
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.54
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.25
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.54
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.86
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.59
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.39
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.74
 p-value of test no 169                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.70
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.15
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.32
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4999.05
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.02
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.04
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.31
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.06
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
 p-value of test no 193                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.14
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.22
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.78
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.51
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.59
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 216                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.31
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.37
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3962.26
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.80
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.50
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.78
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.38
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999933929
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.37
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000017839
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.067
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35570
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 7                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5498
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4220
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.07
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    2.15
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.63
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.04
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.18
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.18
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.99
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.07
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.53
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.09
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.21
 p-value of test no 65                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.47
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.42
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.80
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908375
   j =  2                              :            45805
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908065
   j =  2                              :            45963
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.054
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.87
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.49
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.21
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.19
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.67
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.08
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.92
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.88
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.09
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.68
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.60
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.81
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.69
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.22
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.86
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.89
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.06
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.54
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.45
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.44
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.13
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.26
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.48
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.44
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.74
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.80
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.82
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.08
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.85
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.73
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.76
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.37
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4879.75
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.36
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.02
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.85
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.01
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.10
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.66
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.69
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.06
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.50
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
 p-value of test no 185                :    0.9922
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 187                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.01
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.49
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.55
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.75
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.30
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.94
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.21
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.83
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4167.05
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4077.90
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12001.81
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.86
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.55
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000053953
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.58
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000019111
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 235                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.27
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.36
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35571
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 3                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7118
 p-value of test no 18                 :    0.9905
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.93
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    2.53
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    2.69
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.91
 p-value of test no 46                 :    0.9962
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.21
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.37
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.09
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   97.87
 p-value of test no 52                 :  2.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.50
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.48
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.92
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.64
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7144.43
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.16
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.35
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.04
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4971.63
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45635
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908734
   j =  2                              :            45627
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908478
   j =  2                              :            45758
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.42
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.59
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.24
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.09
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.25
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.26
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.85
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.88
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.75
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.94
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17664.54
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.94
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.74
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.45
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.91
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.21
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.27
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.82
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.76
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.71
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.78
 p-value of test no 157                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.67
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.75
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.30
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.39
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.64
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.72
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.61
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.24
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.53
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.46
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.74
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.19
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.94
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.38
 p-value of test no 172                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.61
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.39
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.46
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.69
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.65
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  8.3e-3
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  242.06
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.92
 p-value of test no 207                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.03
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9771.54
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.093
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.29
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.95
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.23
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.26
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.53
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11616.19
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.81
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999924182
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.23
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999981392
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.83
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  32  CouponCollector, r = 20         2.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35572
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 9                  :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    6.02
 p-value of test no 33                 :  9.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    8.91
 p-value of test no 44                 :  4.6e-5    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.81
 p-value of test no 47                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.26
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.29
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.02
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.44
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.10
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.34
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  378.89
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.62
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7000.20
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.13
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.28
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.84
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.19
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5046.32
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908683
   j =  2                              :            45654
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45758
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869758
   j =  1                              :        399908486
   j =  2                              :            45754
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.44e-4
 p-value of test no 93                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 114                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.34
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.57
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.48
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.33
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.58
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.01
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.42
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.76
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.75
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.29
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17323.96
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.56
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.34
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    5.22
 p-value of test no 149                : 1 -  1.9e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.29
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.62
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.55
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.12
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.12
 p-value of test no 155                :  8.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.58
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.90
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.26
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.55
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.03
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.56
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.28
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.39
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  185.05
 p-value of test no 164                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.51
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.49
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.49
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.74
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.77
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.30
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.07
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.54
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.14
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.46
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.88
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.18
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.50
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.14
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.60
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.24
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.36
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.96
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.94
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.74
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.98
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 216                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.59
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.58
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.29
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.82
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.32
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11737.30
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.08
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999945431
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.94
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000000109
 
 Normal statistic for number of bits   : 8.62e-4
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2S, t = 5         9.7e-4
  25  ClosePairs mNP2, t = 16         4.6e-5
  74  RandomWalk1 R (L=50, r=0)      1 -  1.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35573
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 6                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 10                 :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5566
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7058
 p-value of test no 15                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.47
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.94
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.60
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.88
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.22
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.10
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.06
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.75
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.61
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.43
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.33
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.70
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.48
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.90
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.08
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.21
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907849
   j =  2                              :            46068
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907626
   j =  2                              :            46178
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.17
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.59
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.01
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.33
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.25
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.41
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.03
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.21
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.45
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.10
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.08
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.54
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.70
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.88
 p-value of test no 152                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.08
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.88
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.20
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.82
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.85
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.00
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.54
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.23
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.99
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.02
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.17
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.37
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.07
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.36
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.10
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.72
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.86
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.37
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.27
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.99
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.12
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.82
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.96
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.046
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 185                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.37
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.49
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.36
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.51
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.87
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.24
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.05
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.49
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.85
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.79
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.89
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999987530
 
 Normal statistic for number of bits   :  -0.099
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.79
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000068830
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35574
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 10                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1226
 p-value of test no 11                 : 1 -  7.5e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334346
   j =  1                              :        599997548
   j =  2                              :             1226
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1210
 p-value of test no 12                 : 1 -  1.1e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334330
   j =  1                              :        599997580
   j =  2                              :             1210
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5537
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   18.65
 p-value of test no 46                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.52
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.16
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.34
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.75
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.21
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.77
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.90
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.58
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.70
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.67
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.53
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.62
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.67
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.42
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5122.29
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908632
   j =  2                              :            45681
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45536
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869536
   j =  1                              :        399908930
   j =  2                              :            45532
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 97                 :  3.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-3
 p-value of test no 98                 :    0.9978
 
 Anderson-Darling statistic = A2       :    4.65
 p-value of test no 99                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.77
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.46
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.64
 p-value of test no 122                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.00
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.47
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.42
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.83
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.04
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.47
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17738.54
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.33
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.72
 p-value of test no 147                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.90
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.38
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.47
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.03
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.59
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.36
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.98
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.83
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.37
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.81
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.59
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.83
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.40
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.15
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.88
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.16
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.16
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.25
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.29
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.14
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.41
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.53
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.36
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4918.28
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.27
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.73
 p-value of test no 175                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.93
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.20
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 188                :    0.81
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.05
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.50
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.56
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.88
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.78
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.26
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 223                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5084.76
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.02
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.52
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.99
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11767.83
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.45
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999971066
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.61
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999922346
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.62
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  7.5e-5
  12  CollisionOver, t = 21          1 -  1.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35575
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 3                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5348
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.46
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.76
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 34                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.96
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.68
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.42
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.19
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.62
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.57
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.10
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.88
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.52
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.68
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.90
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.62
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.69
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.35
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5149.23
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908141
   j =  2                              :            45928
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45755
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869755
   j =  1                              :        399908492
   j =  2                              :            45751
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 99                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.26
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.13
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.19
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.82
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.69
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.18
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.75
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.63
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.51
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.75
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.49
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17118.01
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.03
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.03
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.14
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.32
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.15
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.36
 p-value of test no 151                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.52
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.81
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.84
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.53
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.68
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.74
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.83
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.37
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.32
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.66
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.50
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.35
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.00
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.41
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.15
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.31
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.74
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.91
 p-value of test no 170                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.77
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.93
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.14
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.65
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.34
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.47
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.55
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.21
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.36
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.79
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10243.75
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.97
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5056.78
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.08
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.09
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.64
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.10
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.42
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.73
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999909884
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.92
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000058288
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.30
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
 p-value of test no 251                :    0.9902
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.49
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:20.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35576
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 6                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 7                  :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5593
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4403
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.47
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.77
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.42
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.03
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.84
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.69
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.03
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.41
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6985.92
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.26
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 63                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.25
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.33
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.90
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.56
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908173
   j =  2                              :            45912
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908315
   j =  2                              :            45838
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.093
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.91
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.24
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.65
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.52
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   61.01
 p-value of test no 123                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.62
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.01
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.91
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.03
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.66
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.89
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.52
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17655.86
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.02
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.01
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.83
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.89
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.35
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.83
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.68
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.24
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.17
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.97
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.75
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.55
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.96
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.36
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.01
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.53
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.83
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.00
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.53
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.32
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.95
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  249.10
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.31
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.06
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.77
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.59
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.10
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.81
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.32
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.81
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 197                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.66
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.59
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.53
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.78
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.12
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 217                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.97
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.76
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.81
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.86
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.14
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.94
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.66
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000035056
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.65
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999904208
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.079
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:17.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35577
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997257
   j =  2                              :             1370
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4186
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4273
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 20                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.59
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.15
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.79
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.81
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.93
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.60
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.63
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.98
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7079.34
 p-value of test no 57                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.89
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.66
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.76
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.16
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908460
   j =  2                              :            45767
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 115                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.63
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.54
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.21
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.71
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.89
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.06
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.80
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.49
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.12
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.12
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.01
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17823.49
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.60
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.98
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.70
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.34
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.75
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.77
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.11
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.76
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.73
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.55
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.35
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.88
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.53
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.92
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.94
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.67
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.93
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.12
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.26
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.33
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.27
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.58
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.43
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.08
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.00
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.52
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.44
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  442.11
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.04
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.06
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.96e-3
 p-value of test no 190                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.51
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.40
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.14
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10159.51
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.15
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.57
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.86
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.94
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.12
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.90
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.94
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999913601
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999995942
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:06.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35578
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 11                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4449
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.02
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     965
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 45                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.63
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.13
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.47
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.03
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.08
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.01
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.56
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.05
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.53
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   15.11
 p-value of test no 61                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.26
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.27
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.77
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5095.54
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45695
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869695
   j =  1                              :        399908610
   j =  2                              :            45695
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 93                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.49
 p-value of test no 116                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.94
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.15
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.41
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.62
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.41
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 128                :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.28
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.16
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.51
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.56
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17744.59
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.28
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.61
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.99
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.78
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.37
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.75
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.06
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.65
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.87
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.64
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.50
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.90
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.84
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.61
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.39
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.75
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.06
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.64
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.32
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.23
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.59
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.65
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.49
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.98
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.33
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.58
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.47
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.89
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 180                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 186                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.59
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.85
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.76
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.10
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.65
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.93
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.51
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.68
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.25
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.69
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.45
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.76
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.87
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000044413
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000110938
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.79
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:38.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35579
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7484
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7545
 p-value of test no 21                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    2.91
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.89
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.59
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.78
 p-value of test no 49                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.44
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.28
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.88
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  407.07
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1326.45
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.43
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.91
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 63                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.87
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.36
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.79
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5118.44
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907971
   j =  2                              :            46010
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908200
   j =  2                              :            45897
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 108                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.66
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.33
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.43
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.18
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.58
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.00
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 126                :    0.9948
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.01
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.68
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   13.82
 p-value of test no 136                :  1.0e-3    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.14
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.87
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.15
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.75
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.53
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.26
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.07
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   60.09
 p-value of test no 151                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.59
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.13
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.72
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.86
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.44
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.37
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   98.57
 p-value of test no 159                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.61
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.88
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.37
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.25
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.90
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.30
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.52
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.68
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.19
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.51
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.68
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.50
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.15
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4921.34
 p-value of test no 173                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  444.52
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.73
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.11
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 183                :    0.24
 
 Sample variance                       :    2.24
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 192                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.95
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 200                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.14
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.73
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.63
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.58
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.49e-4
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.43
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.55
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.76
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.18
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11792.04
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.28
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.74
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999992453
 
 Normal statistic for number of bits   :  -0.060
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.52
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000054790
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.00
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n91, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:42.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  70  MatrixRank, L=5000              1.0e-3
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35580
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 3                  :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1469
 p-value of test no 5                  :  2.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334589
   j =  1                              :        599997062
   j =  2                              :             1469
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.75
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.29
 p-value of test no 41                 :  2.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    3.41
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.85
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.99
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.25
 p-value of test no 51                 :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.81
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.27
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.91
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1374.96
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.69
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.36
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.63
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.00
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.01
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.71
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45601
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869601
   j =  1                              :        399908801
   j =  2                              :            45595
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908346
   j =  2                              :            45818
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-5
 p-value of test no 110                :    0.9904
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.63
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.03
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.73
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.66
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.84
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.99
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.03
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.40
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.61
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.80
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.65
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.23
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.82
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.76
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.45
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.92
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.12
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.84
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.38
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.48
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.35
 p-value of test no 157                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.35
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.50
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.34
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.65
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.56
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.14
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.32
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.62
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.78
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.60
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.71
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.20
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.21
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.70
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.36
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.72
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.11
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.13
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.83
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 185                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.90
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.55
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  251.74
 p-value of test no 207                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.16
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9854.75
 p-value of test no 215                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.34
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.62
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.15
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4098.66
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.63
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.09
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.36
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000057628
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.96
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999860174
 
 Normal statistic for number of bits   :   -1.11
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    4.67
 p-value of test no 247                :  4.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.89
 p-value of test no 248                :    0.9981
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35581
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5271
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 26                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.28
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.35
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.65
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.92
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.30
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.44
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.31
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.90
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.68
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.77
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.97
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.70
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.94
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.98
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.49
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.45
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908333
   j =  2                              :            45829
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908127
   j =  2                              :            45929
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 84                 :  3.3e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
 p-value of test no 93                 :    0.9965
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 99                 :    0.9999    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.29
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.89
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.17
 p-value of test no 122                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.28
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.33
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.63
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.35
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.86
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17088.35
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.21
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.87
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.89
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.65
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.25
 p-value of test no 150                :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.05
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.25
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.13
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.86
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.35
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.33
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.93
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.03
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.00
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.25
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.90
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.86
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.11
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.21
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.41
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.36
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.70
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.44
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.79
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.00
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.79
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.00
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.93
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.99
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.24
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.00
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.95
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.13
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 202                :    0.9943
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.28
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.11
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.12
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.73
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.11
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.92
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.96
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3860.97
 p-value of test no 228                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.15
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.92
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.97
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999927425
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.96
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000106618
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    1.66
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35582
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 7                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    3.94
 p-value of test no 30                 :  9.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     348
 p-value of test no 37                 :  3.6e-3
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.69
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.77
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.62
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.35
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.55
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.45
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.20
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.71
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1389.43
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.51
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.14
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.30
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.82
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.67
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5156.06
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46374
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870374
   j =  1                              :        399907261
   j =  2                              :            46356
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45576
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869576
   j =  1                              :        399908848
   j =  2                              :            45576
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-5
 p-value of test no 112                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 3.48e-4
 p-value of test no 113                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.09
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.90
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.75
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.14
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.58
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 126                :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.14
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.70
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.33
 p-value of test no 141                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17428.51
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.95
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.58
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.76
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.50
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.36
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.20
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.54
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.42
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.24
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.57
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.17
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.33
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.88
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.39
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.48
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.97
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.33
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.49
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.38
 p-value of test no 165                :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.43
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.96
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.94
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.67
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.06
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.28
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.43
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.54
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.17
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.43
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.43
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.40
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.086
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.91
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.20
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.40
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.06
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.94
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.78
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.61
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4906.05
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.78
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.86
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11896.83
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.57
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.22
 p-value of test no 231                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000016123
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.68
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000005176
 
 Normal statistic for number of bits   :   0.041
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 237                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.08
 
 Sample variance                       :    2.11
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:24.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35583
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7564
 p-value of test no 19                 :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.25
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 27                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9941
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.53
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.47
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.34
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.48
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.27
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.68
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.45
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.20
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.28
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.54
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.82
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.53
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 63                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.85
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.52
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  143.82
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.59
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45438
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869438
   j =  1                              :        399909127
   j =  2                              :            45432
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 90                 :  2.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.89
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.86
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.08
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.69
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.07
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.35
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   17.41
 p-value of test no 134                :  5.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.62
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
 p-value of test no 138                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.24
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17315.48
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.52
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.29
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.61
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.32
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.80
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.91
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.69
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.28
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.22
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.57
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.57
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.65
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.71
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.04
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.73
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.68
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.80
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.97
 p-value of test no 163                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.18
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.50
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.16
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.04
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5280.48
 p-value of test no 168                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.44
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.41
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.67
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.55
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.56
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.10
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.76
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.28
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.04
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    2.22
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.22
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.73
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.74
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.09
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 209                :    0.95
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9828.95
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.93
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.036
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 221                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4725.39
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.39
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.18
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.85
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.01
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.29
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.54
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999979559
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.09
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000088312
 
 Normal statistic for number of bits   :    0.70
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.55
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.87
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.020
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:26.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         5.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35584
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.26
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 39                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.49
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.02
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.51
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.27
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.52
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.00
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.85
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.17
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1547.31
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7250.64
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.55
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
 p-value of test no 63                 :    0.9911
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.78
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.12
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.13
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5241.83
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45349
 p-value of test no 70                 :    0.9934
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869349
   j =  1                              :        399909304
   j =  2                              :            45345
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46052
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870052
   j =  1                              :        399907900
   j =  2                              :            46044
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 2.71e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.15
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.71
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.42
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.36
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.88
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.99
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 132                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.35
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.95
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17690.34
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.06
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.56
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.08
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.33
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.14
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.61
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.06
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.86
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.92
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.66
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.37
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.56
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.22
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.38
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.16
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.04
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.64
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.59
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.52
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.05
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.57
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.97
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.05
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.61
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.09
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.40
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.42
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.87
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.65
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.80
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.40
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.70
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 192                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.18
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.99
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.34
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.08
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.63
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.062
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.83
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4765.32
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.97
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.01
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.49
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11901.01
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.75
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999935951
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.42
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000162004
 
 Normal statistic for number of bits   :    1.28
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
 p-value of test no 245                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.36
 p-value of test no 248                :  9.0e-3
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.19
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35585
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 10                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 11                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5411
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.14
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.83
 p-value of test no 47                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.01
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.12
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.05
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.49
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.11
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.17
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.13
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.94
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.75
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6899.26
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.50
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.72
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.90
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.48
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45840
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869840
   j =  1                              :        399908324
   j =  2                              :            45832
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908262
   j =  2                              :            45866
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.54
 p-value of test no 117                :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.024
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.91
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.05
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.24
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.24
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.70
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.54
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.73
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.80
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.55
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    4.50
 p-value of test no 144                :  5.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17977.84
 p-value of test no 145                :  1.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.41
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.09
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.33
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.59
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.96
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.33
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.47
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.62
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.19
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.81
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.83
 p-value of test no 159                :  6.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.81
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.78
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.74
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.71
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.41
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.80
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.13
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.73
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.87
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.93
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.19
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.84
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.75
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.89
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.11
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.37
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.56
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.10
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.54
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.13
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.92
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.93
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 210                :    0.9924
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10015.42
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.21
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.72
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4703.98
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.70
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.16
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.77
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.26
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.29
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999874607
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.50
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000163630
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 251                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    4.01
 p-value of test no 252                :  9.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.55
 p-value of test no 253                :  5.4e-3
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:23.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35586
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5582
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 15                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.06
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.00
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.07
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.20
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.26
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.25
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.72
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.29
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.44
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.00
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.88
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.86
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.59
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.95
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  172.10
 p-value of test no 67                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.91
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908372
   j =  2                              :            45808
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908066
   j =  2                              :            45961
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 99                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 8.07e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.78
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.37
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.29
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.47
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.42
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.00
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 131                :    0.01
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.13
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.93
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.66
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17167.65
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.19
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.86
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.11
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.81
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.61
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.06
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.16
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.02
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.00
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.51
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.74
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.33
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.02
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.85
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.72
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.36
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.07
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.00
 p-value of test no 166                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.93
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.64
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.98
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.18
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.93
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.06
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.80
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.12
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.01
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.11
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.28
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 180                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.70e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.64
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.53
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.39
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.51
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9929.58
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.57
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.43
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.39
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.68
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.72
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.73
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.01
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999936557
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.84
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999885953
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.88
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:09.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35587
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 12                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 41                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.09
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.72
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.36
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.09
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.52
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.00
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.03
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.36
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.25
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.88
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.85
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.97
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5212.80
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46199
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870199
   j =  1                              :        399907603
   j =  2                              :            46197
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46196
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870196
   j =  1                              :        399907612
   j =  2                              :            46188
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 112                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.35
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.48
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.99
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.66
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.94
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.00
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.74
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.01
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.30
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.16
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.74
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.31
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.25
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   45.05
 p-value of test no 149                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.20
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.20
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.35
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.01
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.45
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.91
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.22
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.89
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.09
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.39
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.64
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.11
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.00
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.56
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.07
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.14
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.08
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.09
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.64
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.69
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.87
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.37
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.26
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.79
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.06
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.90
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.08
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 187                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.52
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.88
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.14
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.02
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.59
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.37
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.69
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.81
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4061.36
 p-value of test no 228                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.20
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11484.18
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.90
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999990287
 
 Normal statistic for number of bits   :  -0.077
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999938090
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.58
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.65
 p-value of test no 240                :  6.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    7.03
 p-value of test no 242                :  3.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.42
 p-value of test no 243                :    0.9997    *****
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:04.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  104  AutoCor, d=3, r=0               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35588
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     172
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.89
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.07
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.26
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.58
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.70
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.17
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.90
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.75
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.02
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1414.56
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.16
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.06
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.91
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.26
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.86
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5278.50
 p-value of test no 68                 :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908695
   j =  2                              :            45651
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908749
   j =  2                              :            45615
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.3e-3
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-3
 p-value of test no 104                :    0.9984
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.04e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.34
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.79
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.84
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.27
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.37
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.76
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.55
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.50
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.54
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.31
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.66
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.49
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.65
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.61
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.31
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.62
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.12
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.61
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.62
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.39
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.15
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.90
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.24
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.10
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.50
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.58
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.26
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.55
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.20
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.05
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.61
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.59
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.67
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.33
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.40
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.16
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.56
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.84
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.57
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.16
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.47
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.54
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 188                :    0.40
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.59
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.18
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.67
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.05
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.74
 p-value of test no 217                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.95
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.19
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4331.97
 p-value of test no 227                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.12
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12251.69
 p-value of test no 229                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11821.03
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.14
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000077917
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.25
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999970007
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 238                :    0.33
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:31.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35589
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.93
 p-value of test no 22                 :  9.6e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.18
 p-value of test no 38                 :    0.9954
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    6.79
 p-value of test no 41                 :  4.8e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.20
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.78
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.99
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.46
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.72
 p-value of test no 51                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.56
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.11
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.86
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.16
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.04
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.81
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.96
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.15
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.12
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.45
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5156.18
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46021
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870021
   j =  1                              :        399907966
   j =  2                              :            46005
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45257
 p-value of test no 71                 :    0.9982
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869257
   j =  1                              :        399909487
   j =  2                              :            45255
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.25
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.24
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.79
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.32
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.20
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.45
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.67
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.10
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.83
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.83
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.11
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.47
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17622.97
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.47
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.44
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.94
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.95
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.94
 p-value of test no 150                :    0.9979
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.57
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.28
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.52
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.72
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.64
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.65
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.14
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.44
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.54
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.43
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.66
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.54
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.61
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.66
 p-value of test no 165                :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.58
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.84
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.81
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.82
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.40
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.42
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.39
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.95
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.63
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.94
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.42
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.89
 p-value of test no 196                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.35
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.98
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.15
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.08
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.51
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.30
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.34
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.15
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.96
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11947.58
 p-value of test no 230                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.07
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000066592
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   91.91
 p-value of test no 233                :  9.9e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999973313
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 243                :    0.06
 
 Sample variance                       :    2.26
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.037
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.52
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:48.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP, t = 16          4.8e-4
  102  Run of bits, r = 27             9.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35590
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 9                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4160
 p-value of test no 16                 :    0.9965
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.78
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9927
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.84
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.34
 p-value of test no 40                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.83
 p-value of test no 46                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.75
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.41
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.58
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.81
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.51
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.56
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.32
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.85
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.20
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-3
 p-value of test no 59                 :    0.9979
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.58
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.60
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.14
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.85
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5032.20
 p-value of test no 68                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908522
   j =  2                              :            45733
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908673
   j =  2                              :            45656
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 90                 :    0.9919
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  9.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.53
 p-value of test no 119                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.74
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.96
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.13
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.97
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.64
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.72
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.08
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.63
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.20
 p-value of test no 134                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.77
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17397.50
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.03
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.47
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.10
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.91
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.91
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.21
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.84
 p-value of test no 154                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.01
 p-value of test no 156                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.82
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.59
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.43
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.68
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.72
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.29
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.20
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.63
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.70
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.42
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.37
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5235.84
 p-value of test no 168                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.39
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.86
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.92
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.17
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.32
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.29
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.82
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.25
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.41
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 183                :    0.76
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.61
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.38
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.72
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.28
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.16
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.86
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.98
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.24
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.09
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.03
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.61
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.72
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.14
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000143179
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.56
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999990176
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:41.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35591
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1490
 p-value of test no 3                  :  4.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334610
   j =  1                              :        599997020
   j =  2                              :             1490
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 5                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 16                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 40                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    4.12
 p-value of test no 44                 :  7.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.66
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.32
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.52
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.85
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.86
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.05
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.01
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.98
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.83
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7274.84
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.26
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.58
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.53
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.17
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.98
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908116
   j =  2                              :            45939
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46354
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870354
   j =  1                              :        399907298
   j =  2                              :            46342
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 83                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 97                 :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 115                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.087
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.68
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.53
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.09
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.91
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.30
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.75
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17608.41
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.88
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.36
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.85
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.51
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.86
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.32
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.09
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.95
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.58
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.16
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.17
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.97
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.34
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.36
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.16
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.63
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.75
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.73
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.51
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.69
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.32
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.35
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.09
 p-value of test no 170                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.56
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.31
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.33
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.51
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.02
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.74
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.21
 p-value of test no 189                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 195                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.60
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.98
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.91
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.11
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.58
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.52
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.27
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.88
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.35
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11444.22
 p-value of test no 229                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.37
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.33
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999923573
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.36
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999908318
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 252                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:23.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35592
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1496
 p-value of test no 3                  :  2.3e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334616
   j =  1                              :        599997008
   j =  2                              :             1496
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7023
 p-value of test no 19                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     972
 p-value of test no 25                 :  9.2e-3
 
 Stat. AD (mNP2)                       :    3.64
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.13
 p-value of test no 34                 :  7.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     287
 p-value of test no 37                 :    0.76
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    2.32
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.14
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.58
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.33
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.03
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.58
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.22
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.71
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.11
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.50
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
 p-value of test no 58                 :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   55.67
 p-value of test no 61                 :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.46
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.53
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.28
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.24
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46018
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870018
   j =  1                              :        399907969
   j =  2                              :            46008
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45384
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869384
   j =  1                              :        399909233
   j =  2                              :            45382
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 74                 :  7.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9966
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.9924
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.89
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.98
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.34
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.35
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.83
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.76
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.22
 p-value of test no 125                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.66
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.61
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.84
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.27
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.69
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.72
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.75
 p-value of test no 146                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.18
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.61
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.32
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.93
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.40
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.64
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.33
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.79
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.47
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.48
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.18
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.77
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.04
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.82
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.26
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.59
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.86
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.00
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.93
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.14
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.87
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.15
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.40
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.59
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.55
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.63
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.31
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.58
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.03
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.51
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.43
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.25
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.49
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.77
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9953.96
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.29
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 219                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5127.17
 p-value of test no 222                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.93
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.54
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.69
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.12
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.25
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.04
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999969866
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.24
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999949610
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.011
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:42.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   3  CollisionOver, t = 2            2.3e-4
  19  BirthdaySpacings, t = 8         0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35593
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.14
 p-value of test no 22                 :    0.9992    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.02
 p-value of test no 28                 :  8.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     129
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.81
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.78
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.40
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.80
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.44
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.33
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.56
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.24
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.82
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.92
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.74
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.07
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.73
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.21
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5107.43
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46249
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870249
   j =  1                              :        399907505
   j =  2                              :            46243
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908122
   j =  2                              :            45936
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 94                 :  9.6e-3
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.94
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.05
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.82
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.17
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.41
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   12.87
 p-value of test no 125                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.55
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.15
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.31
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.49
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.56
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.73
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.44
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.02
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.43
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.35
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.70
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.54
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.54
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.78
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.77
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.18
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.90
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.24
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.03
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.02
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.98
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.11
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.63
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.76
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.46
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.48
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.97
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.45
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.85
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.45
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.23
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.76
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.87
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.86
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 185                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.65
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.23
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.59
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.88
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.11
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10333.65
 p-value of test no 215                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.06
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.18
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.06
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.80
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.57
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.69
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.12
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999942425
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.12
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999963140
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 243                :    0.51
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:00.34
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NP, t = 3            0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35594
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 9                  :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.86
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9918
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.86
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.33
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.97
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.31
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.81
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.02
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.54
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.22
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.45
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.15
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.66
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908267
   j =  2                              :            45862
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46042
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870042
   j =  1                              :        399907917
   j =  2                              :            46040
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 102                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  106.66
 p-value of test no 119                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.24
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.88
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.81
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.54
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.00
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.93
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.96
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.72
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.03
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.46
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17770.22
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.22
 p-value of test no 146                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.23
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.49
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.47
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.05
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.48
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.45
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.69
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.80
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.04
 p-value of test no 155                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.15
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.25
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.22
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.83
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.51
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.45
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.79
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.78
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.18
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.76
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.44
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.70
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.28
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.11
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.17
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.28
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.99
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.33
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.52
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 181                :    0.90
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.52
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.31
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.54
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.59
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.37
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.56
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.79
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.54
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.40
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12133.52
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.60
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.83
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000105664
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.98
 p-value of test no 233                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000100924
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 243                :    0.27
 
 Sample variance                       :    1.91
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.88
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:55.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35595
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5335
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7158
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.00
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.68
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.07
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.03
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.41
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.21
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.21
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.41
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.46
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.88
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.36
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4934.14
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46296
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870296
   j =  1                              :        399907418
   j =  2                              :            46276
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908127
   j =  2                              :            45926
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9901
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
 p-value of test no 104                :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.11
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.51
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.60
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.07
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.83
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.82
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.30
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.71
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.23
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17285.16
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.47
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.18
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.95
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.10
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.66
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.92
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.40
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.46
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.34
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.87
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.35
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.30
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.58
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.46
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.49
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.43
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.34
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.29
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.99
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.90
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.80
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.63
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.50
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.51
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.29
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.50
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.29
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.06
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 188                :    0.06
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.76
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 201                :    0.9949
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.40
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.39
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.74
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.49
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.94
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.53
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.96
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12098.32
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.04
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.53
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000006184
 
 Normal statistic for number of bits   :   0.049
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.23
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000000742
 
 Normal statistic for number of bits   : 5.87e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 238                :    0.30
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:46.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35596
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4498
 p-value of test no 14                 :  7.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4229
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     562
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 35                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.97
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.44
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.33
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.11
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.33
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.59
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.99
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1496.21
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7015.41
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.44
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.12
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.41
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.89
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5402.67
 p-value of test no 68                 :  2.0e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908348
   j =  2                              :            45820
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46340
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870340
   j =  1                              :        399907323
   j =  2                              :            46334
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
 p-value of test no 72                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.023
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.11
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.85
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.90
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.00
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.36
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.61
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.23
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  7.1e-3
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.40
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.81
 p-value of test no 134                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.52
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 143                :  2.0e-4    *****
 
 Anderson-Darling statistic = A2       :    5.01
 p-value of test no 144                :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17905.88
 p-value of test no 145                :  5.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.52
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.21
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.54
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.50
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.84
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.77
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.37
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.93
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.23
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.61
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.35
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.08
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.57
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.42
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.76
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.83
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.40
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.57
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.14
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.35
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.26
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  164.87
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.79
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.69
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.75
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.39
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.71
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.93
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.56
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.48
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.07
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.22
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.52
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.55
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.76
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.42
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.61
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.48
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.27
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.63
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.23
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000007894
 
 Normal statistic for number of bits   :   0.062
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.35
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999919142
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.30
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
 p-value of test no 251                :    0.9981
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.39
 p-value of test no 253                :    0.9917
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:21.76
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  42  Permutation, t = 7              2.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35597
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5515
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.56
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.85
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.02
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.11
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.73
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.92
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.07
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.96
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.83
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.76
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.66
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.25
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.88
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45514
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869514
   j =  1                              :        399908978
   j =  2                              :            45502
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45573
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869573
   j =  1                              :        399908857
   j =  2                              :            45567
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 88                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9961
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 103                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 104                :    0.9928
 
 Anderson-Darling statistic = A2       :    3.17
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.73
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.41
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.49
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.82
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.09
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.38
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.28
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.10
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.81
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 144                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17415.77
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.14
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.95
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.45
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.81
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.39
 p-value of test no 151                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.02
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.80
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.16
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.34
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.78
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.27
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.23
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.02
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.13
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.18
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.67
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.88
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.90
 p-value of test no 164                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.59
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.34
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.24
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.29
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.16
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.58
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.41
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.70
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.39
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.82
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.35
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.53
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.06
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.35
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.82
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.63
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.81
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.42
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.67
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.62
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.52
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.50
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11540.98
 p-value of test no 230                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.01
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000134974
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.38
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999926978
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    0.55
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:28.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35598
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997293
   j =  2                              :             1352
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5312
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.69
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.18
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.77
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.50
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.52
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.98
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.05
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.08
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.10
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.61
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.29
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.04
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.79
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.04
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.66
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.67
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908167
   j =  2                              :            45903
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908300
   j =  2                              :            45844
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 79                 :    0.9953
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.81
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.38
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.41
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.94
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.56
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.47
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.91
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.43
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   16.95
 p-value of test no 134                :  7.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.22
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.81
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.47
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.34
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.39
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.91
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.95
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.79
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.26
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.19
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.78
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.34
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.92
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.71
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.71
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.51
 p-value of test no 161                :  8.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.67
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.27
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.73
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.16
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.28
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.67
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.52
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.08
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.31
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.93
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.90
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.51
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.75
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.71
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.55
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.96
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.39
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.35
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.54
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.19
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.18
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.79
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.13
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.79
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4941.02
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.24
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.15
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.88
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12052.00
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.62
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000200032
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.35
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999845909
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.72
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:09.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  68  MatrixRank, L=1000, r=0         7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35599
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1258
 p-value of test no 3                  :    0.9981
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334378
   j =  1                              :        599997484
   j =  2                              :             1258
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4225
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.92
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.02
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.18
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.55
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.67
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.95
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.58
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.27
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1477.87
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.19
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.74
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   37.61
 p-value of test no 65                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.82
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.62
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5026.35
 p-value of test no 68                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46180
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870180
   j =  1                              :        399907645
   j =  2                              :            46170
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908305
   j =  2                              :            45846
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-4
 p-value of test no 101                :    0.9994    *****
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.73
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.69
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.78
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.14
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.69
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.81
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.65
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.37
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9926
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.82
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.55
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.91
 p-value of test no 141                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17610.56
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.39
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.15
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.29
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.25
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.25
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.85
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.67
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.95
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.30
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.33
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.00
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.13
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.47
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.81
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.08
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.32
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.98
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.22
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.39
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.13
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.00
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.03
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.54
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.74
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.61
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.86
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.59
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5027.07
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.36
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.57
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.15
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.53
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.62
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.35
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.38
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.57
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4850.52
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.59
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.11
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4123.11
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.91
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.02
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.65
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999949613
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.01
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000141898
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 242                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:34.90
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35600
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7146
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7234
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 30                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 34                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.69
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.35
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.78
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.42
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.69
 p-value of test no 51                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.04
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.76
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.19
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6983.84
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.29
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.83
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.29
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.95
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4977.49
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46190
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870190
   j =  1                              :        399907622
   j =  2                              :            46186
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908680
   j =  2                              :            45657
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 102                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.50
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.41
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.54
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.72
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.21
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.63
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.22
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.37
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.45
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.78
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.64
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.24
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.68
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.36
 p-value of test no 151                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.51
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.21
 p-value of test no 156                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.76
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.77
 p-value of test no 158                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.88
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.66
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.43
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.20
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.70
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.83
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.50
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.37
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.37
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5229.45
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.77
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.75
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.67
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.81
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.51
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.20
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.62
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.25
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.68
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    2.27
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.28
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.65
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 208                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10134.65
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9793.17
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.077
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.85
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.60
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.07
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.22
 p-value of test no 228                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.49
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.33
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.63
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000090355
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.21
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000067876
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.08
 
 Sample variance                       :    2.06
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:48.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35601
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 5                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 7                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997056
   j =  2                              :             1472
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 11                 :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 12                 :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.20
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.45
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 36                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    6.89
 p-value of test no 45                 :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.39
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.13
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.85
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.94
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.84
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.36
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.44
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.54
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6837.78
 p-value of test no 57                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.55
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
 p-value of test no 62                 :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.34
 p-value of test no 65                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.35
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.97
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.25
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46138
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870138
   j =  1                              :        399907728
   j =  2                              :            46130
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.23
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.50
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.68
 p-value of test no 122                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.46
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.95
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.09
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.60
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.53
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.80
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.92
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.89
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17208.75
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.24
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.21
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.76
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.60
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.25
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.08
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.62
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.24
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.67
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.95
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.06
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.76
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.51
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.87
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.98
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.61
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.66
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.10
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.44
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.21
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.07
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.26
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  320.27
 p-value of test no 171                :    0.9922
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.42
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4719.89
 p-value of test no 173                :    0.9978
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.65
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.97
 p-value of test no 175                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.00
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.80
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.070
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.30
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.32
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.95
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.80
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.14
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.20
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.13
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4220.58
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.89
 p-value of test no 228                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.71
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.41
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.64
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000111049
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.07
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000085831
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.28
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:24.71
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2S, t = 16        3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35602
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4447
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.56
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    4.22
 p-value of test no 30                 :  6.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     675
 p-value of test no 31                 :  1.4e-3
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.21
 p-value of test no 46                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.16
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.73
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.24
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.47
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.82
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.85
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.53
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.99
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.66
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.45
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.60
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.39
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.88
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.09
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.42
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5024.18
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45994
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869994
   j =  1                              :        399908017
   j =  2                              :            45984
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45811
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869811
   j =  1                              :        399908380
   j =  2                              :            45807
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
 p-value of test no 101                :    0.9901
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.81
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.64
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.77
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.65
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.17
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.53
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.10
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.48
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.96
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.63
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.12
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17482.28
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.16
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.79
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.85
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.62
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.93
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.00
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.01
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.58
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.54
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.06
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.44
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.24
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.64
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.31
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.07
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.79
 p-value of test no 163                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.10
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.06
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.66
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.16
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.09
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.61
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.43
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.41
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.90
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5015.97
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.43
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.34
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.01
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.19
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.72
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.53
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.73
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10216.42
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.14
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.60
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.48
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.09
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.60
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.65
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11577.57
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.70
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999912752
 
 Normal statistic for number of bits   :   -0.69
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999990806
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 248                :    0.88
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:10.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35603
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1483
 p-value of test no 10                 :  7.8e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334603
   j =  1                              :        599997034
   j =  2                              :             1483
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 32                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.61
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.37
 p-value of test no 49                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.85
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.72
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.04
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.05
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.03
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.58
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.31
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.15
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.30
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 64                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.42
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.86
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.46
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5000.66
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907915
   j =  2                              :            46038
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45909
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869909
   j =  1                              :        399908184
   j =  2                              :            45905
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.32
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.40
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.75
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.81
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.67
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.41
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.05
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.85
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.80
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.51
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 144                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17455.99
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.88
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.55
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.79
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.01
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.19
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.54
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.91
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.18
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.47
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.28
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.35
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.10
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.63
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.79
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.04
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.95
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.97
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.17
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.24
 p-value of test no 164                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.63
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.71
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.52
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.02
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.35
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.56
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.61
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.87
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.90
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.20
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.73
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.56
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.87
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.37
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 191                :  4.4e-3
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 192                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.84e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.24
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.45
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.17
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 208                :  8.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9802.28
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.39
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4761.39
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.50
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.75
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.51
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12037.89
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11902.75
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.01
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000080158
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.33
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999937172
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 248                :    0.76
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:46.22
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  10  CollisionOver, t = 14           7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35604
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.11
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 30                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.93
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.59
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.95
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.50
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.68
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.18
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.36
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.82
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.44
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6971.78
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.64
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.28
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.56
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.14
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.64
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907600
   j =  2                              :            46200
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45805
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869805
   j =  1                              :        399908394
   j =  2                              :            45797
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 113                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.79
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.41
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.75
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.60
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.73
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.14
 p-value of test no 129                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 132                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.15
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.56
 p-value of test no 134                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.86
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.21
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.77
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.63
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.43
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.75
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.65
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.41
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 151                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.99
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.84
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.33
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.53
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.16
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.91
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.19
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.71
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.16
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.49
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.30
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.87
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.05
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.06
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.88
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.32
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.18
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.26
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.30
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.81
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.71
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.08
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.07
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.76
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.47
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.60
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.54
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.56
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-3
 p-value of test no 208                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 210                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10391.75
 p-value of test no 211                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9736.79
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 221                :    0.9962
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.21
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.70
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3974.28
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.98
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.98
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.64
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.84
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000055279
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.32
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000040981
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.044
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    2.34
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:02.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35605
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5417
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.13
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.40
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.72
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.52
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.04
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.75
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   84.10
 p-value of test no 53                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.98
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.33
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1329.44
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.11
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-3
 p-value of test no 59                 :    0.9986
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.64
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.46
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.20
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.65
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4901.88
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46050
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870050
   j =  1                              :        399907905
   j =  2                              :            46040
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908163
   j =  2                              :            45914
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 84                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.28e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.32
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.92
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.78
 p-value of test no 120                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.16
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.27
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.44
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.00
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.02
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.92
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.36
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.18
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.65
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.38
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17666.13
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.18
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.26
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.72
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.18
 p-value of test no 150                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.30
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.12
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.04
 p-value of test no 153                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.10
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.76
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.63
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.02
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.82
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.73
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.38
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.44
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.07
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.49
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.60
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.66
 p-value of test no 165                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.26
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.77
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.39
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.82
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.75
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.32
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.43
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.20
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.43
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.00
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.89
 p-value of test no 178                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.36
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 185                :  6.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.76
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 205                :    0.86
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.06
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.85
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.31
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.075
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.52
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.29
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.21
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.84
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11975.78
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.34
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.65
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000132064
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.30
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999954788
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 236                :    0.04
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 242                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.67
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:07.06
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35606
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 8                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.22
 p-value of test no 40                 :  8.8e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 45                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.31
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.06
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.95
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.02
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.15
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  189.86
 p-value of test no 54                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.49
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.44
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6858.08
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.75
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.78
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.90
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.15
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.30
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908027
   j =  2                              :            45982
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908672
   j =  2                              :            45658
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 92                 :    0.9954
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 105                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.25
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.55
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.81
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.38
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.25
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.94
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.51
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.30
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.53
 p-value of test no 135                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.66
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17268.37
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.04
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.44
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.83
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.26
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.89
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.36
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.79
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.18
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.19
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.34
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.56
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.79
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.79
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.61
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.10
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.12
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.06
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.35
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.01
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5168.39
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.32
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.52
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.69
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.03
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.59
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.69
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.16
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.42
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.51
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.21
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
 p-value of test no 201                :    0.9975
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  160.30
 p-value of test no 203                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.31
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.33
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9796.35
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.88
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.78
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.82
 p-value of test no 227                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.81
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11632.08
 p-value of test no 229                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.12
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.57
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000165202
 
 Normal statistic for number of bits   :    1.31
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.59
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999947435
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
 p-value of test no 245                :    0.9969
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.31
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.33
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:47.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NP, t = 16           8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35607
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 12                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.93
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.73
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.63
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.93
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.21
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.09
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.17
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.56
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  380.93
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.89
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6925.18
 p-value of test no 57                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.27
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.88
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.32
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.36
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.15
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45550
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869550
   j =  1                              :        399908902
   j =  2                              :            45546
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 83                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 109                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.090
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.65
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.70
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.11
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.46
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.52
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.34
 p-value of test no 124                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.22
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.94
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.28
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.08
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
 p-value of test no 143                :    0.9910
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17062.52
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.03
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 147                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.63
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.42
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.05
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.09
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.19
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.91
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.00
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.94
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.58
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.07
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.48
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.44
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.95
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.21
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.44
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.68
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.62
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.92
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.90
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.65
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.56
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.56
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.93
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.49
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.71
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.44
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.35
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 182                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.23
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.33
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.59
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.03
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.27
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.92
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9674.65
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.40
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.61
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.72
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.40
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12362.45
 p-value of test no 229                :  2.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.84
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.51
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999940175
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.27
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999843488
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 236                :    0.9938
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.83
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.85
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:48.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  99  HammingIndep, L=1200, r=0       2.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35608
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 8                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4438
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 28                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.66
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.07
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.44
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.80
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.61
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.13
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.26
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.32
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.58
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.80
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7102.07
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.38
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.41
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.77
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.53
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908091
   j =  2                              :            45953
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46053
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870053
   j =  1                              :        399907895
   j =  2                              :            46051
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 88                 :    0.9993    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.058
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 118                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.17
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.73
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.62
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.79
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.69
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.16
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.90
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.40
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 136                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.64
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17449.57
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.27
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.44
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.48
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.53
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.03
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.18
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.20
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.80
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.65
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.49
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.30
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.68
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.32
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.99
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.54
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.73
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.13
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.18
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.90
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.08
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.87
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.26
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.16
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.53
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.21
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.55
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.28
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.54
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9954
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.09
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.26
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.51
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.36
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.20
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.42
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5059.20
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.14
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.59
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.45
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.29
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12012.52
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.79
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000089410
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.77
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000105088
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 241                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.052
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35609
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 16                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.57
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    4.55
 p-value of test no 44                 :  4.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.94
 p-value of test no 46                 :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.30
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.22
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.22
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.24
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.81
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.03
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.59
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.19
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.72
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.10
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7280.47
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.91
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.51
 p-value of test no 65                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.64
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.55
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.72
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908021
   j =  2                              :            45985
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45878
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869878
   j =  1                              :        399908245
   j =  2                              :            45876
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 83                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 91                 :    0.9970
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 94                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 101                :    0.73
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.64
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.96
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.70
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.42
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.56
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.64
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.98
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.71
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 137                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
 p-value of test no 138                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.06
 p-value of test no 141                :  8.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.34
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.10
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.00
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.86
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.76
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.38
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.48
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.43
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.22
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.05
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.27
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.22
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.78
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.37
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.51
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.45
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.95
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.80
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.53
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.73
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.38
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.80
 p-value of test no 167                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.82
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.30
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.82
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.04
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.98
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.71
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.04
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.04
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.02
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.11
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.02
 p-value of test no 178                :    0.9954
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.52
 p-value of test no 198                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.21
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.96
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.67
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.50
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.53
 p-value of test no 222                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.09
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.01
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3935.67
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.54
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11803.51
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.85
 p-value of test no 231                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000113995
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.51
 p-value of test no 233                :  7.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999966443
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.06
 p-value of test no 249                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.034
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35610
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 10                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5569
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 16                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.57
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.92
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.48
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.12
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.54
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.76
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  477.80
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.66
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7304.27
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.17
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.27
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.85
 p-value of test no 66                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.41
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4944.90
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908162
   j =  2                              :            45913
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.89
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.27
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.68
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.09
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 124                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.24
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.05
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.59
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.71
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.39
 p-value of test no 136                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.59
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17430.92
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.19
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.24
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.34
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.22
 p-value of test no 149                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.26
 p-value of test no 150                :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.21
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   13.62
 p-value of test no 152                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.62
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.70
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.13
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.10
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.02
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   95.92
 p-value of test no 159                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.72
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.26
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.48
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  427.56
 p-value of test no 163                :    0.9916
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.63
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.41
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  474.56
 p-value of test no 166                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.60
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.25
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.88
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.65
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.73
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.75
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.64
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.76
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.88
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.08
 p-value of test no 176                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.11
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.83
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.23
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.59
 p-value of test no 198                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.05
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.33
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.64
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.24
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.091
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.03
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.75
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.12
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.11
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.30
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.79
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.91
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999911120
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.47
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000048943
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.59
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 M (L=50, r=25)      0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35611
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7095
 p-value of test no 18                 :    0.9956
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.08
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.93
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     181
 p-value of test no 43                 :  7.6e-3
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.85
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 47                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.72
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.46
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.18
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.58
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.71
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.62
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.02
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.45
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.50
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.60
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.85
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.62
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.45
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4891.14
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908659
   j =  2                              :            45666
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908646
   j =  2                              :            45671
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.74
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.53
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.89
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.58
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.64
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.26
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.19
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.65
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.13
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17542.36
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.84
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.92
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.30
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.70
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.96
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.42
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.03
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.07
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.55
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.63
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.31
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.97
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.85
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.21
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.73
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.60
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.47
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.65
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.34
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.46
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.47
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5098.19
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.56
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.94
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.13
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.46
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.14
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.66
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.47
 p-value of test no 175                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.66
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.54
 p-value of test no 177                :    0.9945
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.80
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.00
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.28
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.60
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9821.47
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.89
 p-value of test no 216                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 217                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.60
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.72
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.66
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.52
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.03
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.18
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.27
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999961931
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.02
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000109846
 
 Normal statistic for number of bits   :    0.87
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 253                :    0.23
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35612
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4466
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.36
 p-value of test no 29                 :  6.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    3.80
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.18
 p-value of test no 34                 :  2.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.58
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.22
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.07
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.09
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.65
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.73
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7062.87
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.06
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.77
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.55
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.62
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5074.02
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908405
   j =  2                              :            45790
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908132
   j =  2                              :            45928
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.61e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.81
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.18
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.33
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.40
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.11
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.06
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.23
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.76
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.02
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17589.02
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.72
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.60
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.38
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.42
 p-value of test no 151                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.68
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.82
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.31
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.51
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.08
 p-value of test no 157                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.11
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.44
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.59
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.40
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.40
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.29
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.81
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.79
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.76
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.58
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.76
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.57
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.46
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.40
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4791.05
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.22
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.61
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.24
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.58
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.40
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.42
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.00
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.17
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 209                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    5.08
 p-value of test no 210                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10419.25
 p-value of test no 211                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.00
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.43
 p-value of test no 218                :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5060.79
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4684.67
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.54
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.63
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11565.57
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11776.11
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.77
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999905789
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.95
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999919478
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.74
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35613
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7504
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7472
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     651
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.87
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.77
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.61
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.71
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.57
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.37
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.75
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.49
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.01
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.84
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.19
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.82
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.77
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.00
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.66
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.89
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.92
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908475
   j =  2                              :            45758
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908661
   j =  2                              :            45668
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.63
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.31
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.44
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.32
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.46
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.63
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.47
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.55
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.44
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.71
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.68
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17378.48
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.22
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   54.39
 p-value of test no 147                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.15
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.09
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.87
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.30
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.61
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.75
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.79
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.49
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.53
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.84
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.35
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.46
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.24
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.85
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.29
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.94
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.01
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.79
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.99
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.12
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.05
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.24
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.70
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.30
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.05
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.60
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.98
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.29
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.76
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 193                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 195                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.56
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
 p-value of test no 201                :    0.9935
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 202                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.32
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.44
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.97
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.48
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.44
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.81
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.67
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.72
 p-value of test no 228                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.77
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11953.46
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.53
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999974033
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.21
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000022849
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.59
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.11
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35614
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     973
 p-value of test no 25                 :  8.4e-3
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    3.18
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.34
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.32
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.69
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.31
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.47
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.50
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.82
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.84
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.81
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.14
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.36
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.78
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.92
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.69
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.96
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.32
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.81
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.10
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45666
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869666
   j =  1                              :        399908674
   j =  2                              :            45654
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908792
   j =  2                              :            45598
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 94                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.44
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.54
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.11
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.80
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.93
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.67
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.56
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.51
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.81
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17507.86
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.60
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.33
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.71
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.33
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.63
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.84
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.79
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.29
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  187.86
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.01
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.39
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.46
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.49
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.08
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.93
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.45
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.93
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.88
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.44
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.04
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.23
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.28
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.05
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.90
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.97
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.80
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.81
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 188                :    0.38
 
 Sample variance                       :    1.21
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.57
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9929
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.87
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10237.05
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 213                :    0.88
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9751.99
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.063
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.77
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.04
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.16
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.98
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.77
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.98
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.01
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000025351
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.71
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999946244
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 243                :    0.40
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35615
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.54
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.70
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 45                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.52
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.84
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.15
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.41
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.52
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.42
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.95
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.23
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.74
 p-value of test no 59                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    3.76
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.10
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.18
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.71
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.09
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.66
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908183
   j =  2                              :            45904
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908233
   j =  2                              :            45882
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-3
 p-value of test no 76                 :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.45e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.52
 p-value of test no 118                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.83
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.04
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.48
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.34
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.57
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.32
 p-value of test no 124                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.72
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 128                :    0.9974
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.53
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.93
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.65
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17349.20
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.83
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.64
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.84
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.65
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.13
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.31
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.95
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.18
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.21
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.94
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.67
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.51
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.59
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.20
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.74
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  190.17
 p-value of test no 164                :  1.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.84
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.82
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.29
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.37
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.09
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.56
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.06
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.77
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.83
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.41
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.82
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.76
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.26
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.47
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.65
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.79
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.89
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.23
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.97
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-3
 p-value of test no 209                :    0.9980
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9724.16
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.32
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.37
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 225                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.60
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.02
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.90
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.81
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.77
 p-value of test no 230                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.46
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999932777
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.63
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000079225
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9972
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35616
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  9.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 5                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7446
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    4.83
 p-value of test no 30                 :  3.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     658
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    3.41
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    3.15
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.22
 p-value of test no 41                 :  7.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.73
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.17
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.01
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.00
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.68
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.41
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.10
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.24
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.98
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7162.23
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.96
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.35
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.71
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.05
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.56
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45832
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869832
   j =  1                              :        399908345
   j =  2                              :            45814
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908476
   j =  2                              :            45756
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 116                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.91
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.92
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.40
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.48
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.28
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.80
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.46
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.97
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.19
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.02
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17785.78
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.86
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.60
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.37
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.25
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.23
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   55.35
 p-value of test no 153                :  4.4e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.09
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.32
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.32
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.59
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.50
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.17
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.24
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.95
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.22
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.43
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.75
 p-value of test no 164                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.01
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.88
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.00
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.77
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.54
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.53
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.97
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.44
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.41
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.85
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.13
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.52
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.81
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.70
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.38
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  252.26
 p-value of test no 207                :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.28
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.12
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4709.16
 p-value of test no 222                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 225                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.41
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.19
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.95
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.87
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.64
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.10
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000138439
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.11
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999977090
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    0.49
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.078
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.37
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:54.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35617
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     859
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 32                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.62
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.48
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.70
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.44
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1594.60
 p-value of test no 56                 :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.49
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.46
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.65
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.31
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5133.71
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908019
   j =  2                              :            45983
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45939
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869939
   j =  1                              :        399908124
   j =  2                              :            45935
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 73                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 8.90e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.52
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.91
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.10
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.92
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.95
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.76
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 130                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.75
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.41
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.13
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17656.63
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.19
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.74
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.62
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.89
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.54
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    7.58
 p-value of test no 154                :    0.9994    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.91
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.98
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.44
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.04
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.01
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.72
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.15
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.91
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.09
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.65
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.31
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.82
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.98
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.60
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.39
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.02
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.40
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.36
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.38
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.75
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.50
 p-value of test no 175                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.66
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.12
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.57
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.15
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.28
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.23
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.78
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.97
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.27
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.56
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.50
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.07
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.95
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999949412
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.93
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000053545
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:35.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 R (L=50, r=25)      0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35618
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5465
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    2.88
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    2.65
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.51
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.22
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.45
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.12
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.76
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.85
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.54
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.57
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.15
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6980.84
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.60
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.80
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.23
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.45
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.78
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907887
   j =  2                              :            46049
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908636
   j =  2                              :            45679
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 90                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.48e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 111                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.068
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.17
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.66
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.91
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.91
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.90
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.63
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.76
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.32
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.12
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.24
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.54
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.99
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.12
 p-value of test no 149                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.86
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.16
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.37
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.40
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.29
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.98
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.96
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.61
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.98
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.20
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.82
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.13
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.22
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.01
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.49
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.37
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.94
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.29
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.21
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.21
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.81
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.55
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.10
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.32
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.59
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.62
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.56
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.62
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.17
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.32
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.45
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10082.47
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.43
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9961
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.94
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4260.57
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.71
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11756.73
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11996.96
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.39
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999983720
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.42
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000248272
 
 Normal statistic for number of bits   :    1.96
 p-value of test no 234                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 253                :    0.04
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:25.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35619
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 20                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     930
 p-value of test no 25                 :    0.16
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 40                 :    0.9906
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.69
 p-value of test no 41                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.19
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.76
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.63
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.33
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.99
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.95
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.00
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.08
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1340.56
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.44
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.64
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.01
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.65
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.54
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4803.19
 p-value of test no 68                 :    0.9913
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45956
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869956
   j =  1                              :        399908090
   j =  2                              :            45952
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45319
 p-value of test no 71                 :    0.9956
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869319
   j =  1                              :        399909365
   j =  2                              :            45313
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.28
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.41
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.58
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.20
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.12
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.90
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.40
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.57
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.83
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.44
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.04
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.16
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.47
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.96
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.98
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.50
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.26
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.48
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.29
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.85
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.60
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.42
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  580.09
 p-value of test no 158                :  7.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.74
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.78
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.04
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.44
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.60
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.43
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.82
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.92
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.91
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.11
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.99
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.70
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.57
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.33
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4864.61
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.43
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.55
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.01
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 201                :    0.9942
 
 Anderson-Darling statistic = A2       :    3.86
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  150.21
 p-value of test no 203                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.25
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.17
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.64
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.031
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.69
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.16
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.34
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.26
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.30
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11511.58
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.18
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000169858
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.48
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999940493
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:16.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35620
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.13
 p-value of test no 36                 :    0.9995    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.55
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.04
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.00
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.49
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.12
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.93
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.36
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7174.61
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.92
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.33
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   15.52
 p-value of test no 66                 :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.64
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.09
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 70                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907915
   j =  2                              :            46041
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45435
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869435
   j =  1                              :        399909136
   j =  2                              :            45423
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  5.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 76                 :    0.9964
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.01
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.47
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.27
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.30
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.11
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.18
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 127                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 128                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.19
 p-value of test no 129                :  5.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.68
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.14
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.43
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.47
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.37
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.97
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.63
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.73
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.73
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.58
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.61
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.18
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.96
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.99
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.14
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.17
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.43
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.94
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.83
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.77
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.41
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.73
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.52
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.78
 p-value of test no 169                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.92
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.87
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.62
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.66
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.36
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.95
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.72
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.89
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.23
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.63
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 202                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.70
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.32
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.52
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.93
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.63
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 223                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5076.14
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.19
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.68
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11392.32
 p-value of test no 229                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.05
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.76
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999993374
 
 Normal statistic for number of bits   :  -0.052
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.89
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000015886
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 238                :    0.94
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:28.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35621
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1231
 p-value of test no 12                 :    0.9999    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334351
   j =  1                              :        599997538
   j =  2                              :             1231
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4179
 p-value of test no 14                 :    0.9918
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9979
 
 Stat. AD after spacings (mNP2-S)      :    2.26
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.96
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.87
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.97
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.60
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.45
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.83
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.23
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.48
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.82
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.33
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.23
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.80
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.65
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.97
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.80
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.45
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.38
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45592
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869592
   j =  1                              :        399908820
   j =  2                              :            45584
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46031
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870031
   j =  1                              :        399907939
   j =  2                              :            46029
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.58
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.99
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.42
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.84
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.49
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.46
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.43
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.18
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.43
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.29
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.18
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17355.26
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.60
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.42
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.71
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.43
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.85
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.74
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.02
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.67
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.97
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.05
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.51
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.89
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.09
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.29
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.48
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.68
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.26
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.67
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.25
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.79
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4804.88
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.04
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.71
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.76
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.29
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.00
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.19
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.01
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.29
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.16
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.35
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.057
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.06
 p-value of test no 196                :    0.9978
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.00
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.63
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.33
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10098.65
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.21
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.31
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.99
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.88
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12119.77
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11831.67
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.77
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000083533
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.93
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999979802
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.17
 p-value of test no 239                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.56
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.29
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35622
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 5                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 6                  :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5527
 p-value of test no 13                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.99
 p-value of test no 23                 :  9.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    5.49
 p-value of test no 32                 :  1.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    4.44
 p-value of test no 45                 :  5.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.03
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   37.83
 p-value of test no 48                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.65
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.84
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.80
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.94
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.44
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.25
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6901.41
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
 p-value of test no 59                 :    0.9977
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.83
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.47
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.04
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.40
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.38
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908450
   j =  2                              :            45763
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 99                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.63
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.51
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.41
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.21
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.30
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.08
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.90
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.46
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.45
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17163.72
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.80
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.78
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.63
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.63
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.02
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.63
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.05
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.82
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.51
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.43
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.05
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.56
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.57
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.56
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.12
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.37
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.96
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.83
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.03
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.52
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.29
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.40
 p-value of test no 168                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.65
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.86
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.81
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.19
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4831.12
 p-value of test no 173                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.60
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.48
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.55
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.72
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
 p-value of test no 186                :    0.9980
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.97
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.42
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.61
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.69
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.16
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.24
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.93
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3933.08
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11793.33
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11517.30
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.22
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000079396
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.88
 p-value of test no 233                :  5.7e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000219547
 
 Normal statistic for number of bits   :    1.74
 p-value of test no 234                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 251                :  3.7e-3
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:27.28
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35623
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    2.65
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.41
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.28
 p-value of test no 46                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.67
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.52
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.38
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.12
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.32
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.85
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.75
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7259.93
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.83
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.05
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.74
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.24
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.76
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908483
   j =  2                              :            45757
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908282
   j =  2                              :            45853
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.17
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.54
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.97
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.28
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.35
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.69
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.93
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.94
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.17
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.21
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.36
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.09
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.57
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.44
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.92
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.48
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.03
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.88
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.34
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.75
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.19
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.64
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.97
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.25
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.49
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.79
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.31
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.91
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.81
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.69
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.82
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.69
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.65
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.72
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.57
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.40
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.90
 p-value of test no 172                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.94
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.51
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.86
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.48
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.20
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.28
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.43
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.57
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.73
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.78
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.47
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.04
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.46
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4032.74
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.81
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.37
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.77
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999937886
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.42
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000075115
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.79
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
 p-value of test no 241                :    0.9950
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 248                :    0.82
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.35
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:13.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35624
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 10                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4218
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.49
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.87
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.94
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.12
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.13
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.90
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.68
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.22
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.87
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.49
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.21
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.89
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.28
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.52
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.82
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.16
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399907996
   j =  2                              :            46002
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45479
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869479
   j =  1                              :        399909046
   j =  2                              :            45471
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 74                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 90                 :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
 p-value of test no 91                 :    0.9955
 
 Anderson-Darling statistic = A2       :    5.40
 p-value of test no 92                 :  1.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.81
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.65
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.43
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.17
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.38
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.68
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.24
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.51
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17354.54
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.03
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.99
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.21
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.02
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.88
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.32
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.35
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.00
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.40
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.05
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.00
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.94
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.42
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.87
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.19
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.20
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.57
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.12
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.25
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.46
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.84
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.61
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.06
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.59
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.66
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.73
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.90
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.38
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.73
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.22
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.01
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.60
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   41.00
 p-value of test no 197                :  2.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.52
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.50
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.50
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.45
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.62
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.64
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.64
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.91
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.52
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11548.60
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.19
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.83
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  7999835952
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.43
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000065773
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    2.38
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.06
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.48
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35625
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997223
   j =  2                              :             1387
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 23                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9966
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.07
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.56
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.74
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.86
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.43
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.79
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.65
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.69
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.78
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6906.86
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.09
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.77
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.86
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4851.09
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 70                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908321
   j =  2                              :            45835
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908023
   j =  2                              :            45984
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.52e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.71
 p-value of test no 119                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.30
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.62
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.71
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.65
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.54
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.56
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.66
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.18
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.87
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17637.63
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.43
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.80
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.87
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.66
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.44
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.31
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.31
 p-value of test no 156                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.72
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.96
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.05
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.48
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.72
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.73
 p-value of test no 162                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.20
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.03
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.40
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.52
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.16
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.12
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.74
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  159.53
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.93
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.98
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.23
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.92
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.04
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.75
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.68
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.01
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.15
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.12
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.49
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.96
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.096
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.61
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.88
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.91
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.16
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.03
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.72
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.27
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999986279
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.93
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999905279
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.77
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-3
 p-value of test no 245                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 248                :    0.07
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 253                :    0.95
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:47.82
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35626
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     665
 p-value of test no 31                 :  4.7e-3
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.11
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.40
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.23
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.38
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.89
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.08
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.63
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.23
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.96
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.24
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.77
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-3
 p-value of test no 59                 :    0.9974
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.64
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.35
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.46
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.18
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.73
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45767
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869767
   j =  1                              :        399908470
   j =  2                              :            45759
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45752
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869752
   j =  1                              :        399908498
   j =  2                              :            45748
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.080
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.46
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.63
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.83
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.02
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.56
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.76
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.32
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.10
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.96
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.31
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.63
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.71
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17191.27
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.96
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.59
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.49
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.96
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.47
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.42
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.28
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.09
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.45
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.18
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.33
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.48
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.87
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.30
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.44
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.98
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.55
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.73
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.28
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.48
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.91
 p-value of test no 168                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.90
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.71
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.41
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.83
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.97
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.61
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.14
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.92
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.80
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.88
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.71
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.58
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9879.64
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.61
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4961.81
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.40
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.88
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4196.14
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.17
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11628.10
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.55
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000185680
 
 Normal statistic for number of bits   :    1.47
 p-value of test no 232                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.73
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000062299
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-3
 p-value of test no 236                :    0.9968
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.41
 p-value of test no 238                :    0.9920
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.09
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:38.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35627
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9994    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 3                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5321
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.23
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 29                 :    0.9932
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 38                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.11
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.82
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.79
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.39
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.10
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.75
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.48
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.19
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.18
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.74
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.63
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.99
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.64
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4998.77
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908999
   j =  2                              :            45490
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907602
   j =  2                              :            46193
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 104                :  9.3e-4    *****
 
 Anderson-Darling statistic = A2       :    3.96
 p-value of test no 105                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.52
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.09
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.87
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.16
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.32
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.29
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.03
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
 p-value of test no 126                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.19
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.97
 p-value of test no 133                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 140                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.54
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17045.34
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.59
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.95
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.18
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.26
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.05
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.91
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.14
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.41
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.23
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.56
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.72
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.49
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.52
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.59
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.37
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.60
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.87
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  180.97
 p-value of test no 164                :  6.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.01
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.48
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.02
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4766.44
 p-value of test no 168                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  439.96
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.61
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.67
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.54
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.58
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.13
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.71
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.57
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.33
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.10
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.96
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.65
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.48
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.98
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.33
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.67
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.81
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.45
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.50
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.16
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000154432
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.59
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999919577
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
 p-value of test no 236                :    0.9957
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.73
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.097
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:49.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   2  SerialOver, r = 22              0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35628
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5304
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.73
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.79
 p-value of test no 47                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.74
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.15
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.74
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.49
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.86
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.11
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  470.52
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.65
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7064.92
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.29
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.77
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.13
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4933.45
 p-value of test no 68                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908085
   j =  2                              :            45956
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908817
   j =  2                              :            45584
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 83                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.76
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.84
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.94
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.78
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.93
 p-value of test no 122                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.01
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.16
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.21
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.64
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.36
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.05
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.38
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17470.19
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.56
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.85
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.90
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.55
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.31
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.54
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.02
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.31
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 154                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.27
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.25
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.50
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.72
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.92
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.47
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.41
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.22
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.97
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.01
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.99
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  474.91
 p-value of test no 167                :  1.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.67
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.01
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.04
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.49
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.94
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.90
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.96
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.43
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.27
 p-value of test no 176                :  9.8e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.68
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.07
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.76
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.25
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9841.28
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 214                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.50
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5051.49
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.91
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.00
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.27
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.31
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.04
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.15
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999841121
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.07
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000078046
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 248                :    0.05
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:51.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35629
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 28                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.58
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.93
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.98
 p-value of test no 50                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.29
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.51
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.79
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.78
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.19
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.40
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6907.05
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.97
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.71
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.59
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.07
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4940.49
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907568
   j =  2                              :            46216
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908128
   j =  2                              :            45930
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-3
 p-value of test no 80                 :    0.9984
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 93                 :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.55
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.62
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.04
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.19
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.52
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.25
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.38
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.62
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.02
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.82
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 137                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.74
 p-value of test no 141                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17075.90
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.12
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.88
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.75
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.86
 p-value of test no 152                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.21
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.81
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.81
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.40
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.62
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.05
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.14
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.45
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.08
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.66
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.98
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.92
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.39
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.25
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.46
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.57
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.11
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.05
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4856.30
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.87
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.56
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.11
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.87
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.33
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.61
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 182                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.39
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.00
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.96
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.12
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.11
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.32
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.69
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.00
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.99
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.12
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.80
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.38
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.00
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999956876
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.12
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999995108
 
 Normal statistic for number of bits   :  -0.039
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:33.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35630
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5261
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4485
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    3.42
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     546
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 38                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.28
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.96
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.34
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.14
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.43
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.05
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.08
 p-value of test no 53                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.58
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.13
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1425.78
 p-value of test no 56                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.34
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 58                 :  4.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.94
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.64
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.93
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.26
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.42
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907838
   j =  2                              :            46075
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908572
   j =  2                              :            45705
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.28
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.47
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.67
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.26
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.93
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.42
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.98
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.62
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.41
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.23
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.14
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.24
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.62
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.89
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.23
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.78
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.58
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.14
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.03
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.58
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.23
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.43
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.44
 p-value of test no 165                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.01
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.90
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.88
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.79
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.71
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.12
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.07
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.67
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.23
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.93
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.20
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.88
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.21
 p-value of test no 183                :    0.01
 
 Sample variance                       :    2.02
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.29
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.23
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.74
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 204                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.94
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 209                :    0.82
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.15
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.70
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.74
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.65
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.07
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.94
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.34
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.13
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000007870
 
 Normal statistic for number of bits   :   0.062
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.16
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000040531
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.18
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 250                :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.54
 p-value of test no 253                :  5.5e-3
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:28.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35631
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 4                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 5                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.25
 p-value of test no 23                 :  2.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    3.18
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.54
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.71
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.23
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.44
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.13
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.44
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.29
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.72
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.71
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.77
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.06
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.79
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.94
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.95
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.96
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.78
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.04
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5223.54
 p-value of test no 68                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46294
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870294
   j =  1                              :        399907416
   j =  2                              :            46286
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45275
 p-value of test no 71                 :    0.9976
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869275
   j =  1                              :        399909452
   j =  2                              :            45271
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 83                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 85                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 108                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.48
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.81
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.50
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.75
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.58
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.60
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.70
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.88
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.13
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  133.89
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.53
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.25
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.14
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.71
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.37
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.48
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.76
 p-value of test no 151                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.16
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.39
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.65
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.53
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.14
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.21
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.61
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.28
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.50
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.36
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.98
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.90
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.77
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.57
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.21
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.39
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.92
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.51
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.78
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.15
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.22
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.39
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.24
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.45
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.38
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.08
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.72
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.75
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.87
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.65
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.86
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4728.53
 p-value of test no 226                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.03
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.21
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.44
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11790.57
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.60
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000071827
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.81
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000023926
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:47.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35632
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1475
 p-value of test no 5                  :  1.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334595
   j =  1                              :        599997050
   j =  2                              :             1475
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.11
 p-value of test no 35                 :  8.0e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.35
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.54
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.32
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.27
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.84
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.87
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.78
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.89
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.18
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6986.25
 p-value of test no 57                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.27
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.60
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.10
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.72
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908731
   j =  2                              :            45627
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45728
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869728
   j =  1                              :        399908549
   j =  2                              :            45718
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 80                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 86                 :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 88                 :  9.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 89                 :    0.9970
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.77e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.17
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.27
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.62
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.01
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.78
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.20
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.53
 p-value of test no 126                :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    5.44
 p-value of test no 128                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.03
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.21
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.57
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 139                :  3.6e-3
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.24
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17665.12
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.02
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.02
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.90
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.51
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.37
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.57
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.31
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.78
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.01
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.90
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.12
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.10
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.31
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.36
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.63
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.34
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.33
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.92
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.55
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.75
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.64
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.38
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.53
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.42
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.60
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5207.00
 p-value of test no 173                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  322.46
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.12
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.70
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.37
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.52
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.06
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.32
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 209                :    0.9956
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9731.00
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.52
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4908.23
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.69
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.99
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.75
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.54
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.38
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.09
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999971852
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.07
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000173818
 
 Normal statistic for number of bits   :    1.37
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 242                :    0.9993    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:46.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35633
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9917
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    2.75
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.98
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.95
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.15
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.47
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.99
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.75
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.88
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.92
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.63
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1497.44
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.09
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.74
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.94
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.99
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.23
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45963
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869963
   j =  1                              :        399908078
   j =  2                              :            45955
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907929
   j =  2                              :            46031
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-5
 p-value of test no 113                :    0.9954
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.022
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.49
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.88
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.82
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.09
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.23
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.61
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.44
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 126                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.04
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.11
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 136                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.15
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.80
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.86
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.73
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.31
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.71
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.06
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.55
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.12
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.29
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.93
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.26
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.04
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.31
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.07
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.89
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.07
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.06
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.70
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5035.88
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  463.43
 p-value of test no 169                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.35
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.01
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.30
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4756.01
 p-value of test no 173                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.59
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.25
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.26
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.05
 p-value of test no 178                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.22
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.36
 
 Sample variance                       :    1.48
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.95
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.50
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.57
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.46
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10259.63
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.07
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.44
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.52
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.98
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.91
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.56
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.22
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999923981
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.37
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999963890
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:54.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35634
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 4                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 12                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5469
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 14                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4467
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7166
 p-value of test no 18                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.78
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     841
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    2.15
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.96
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.64
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.73
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.45
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  482.59
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.92
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6869.07
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.52
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.55
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.09
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  145.54
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4738.83
 p-value of test no 68                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45864
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869864
   j =  1                              :        399908275
   j =  2                              :            45858
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46201
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870201
   j =  1                              :        399907601
   j =  2                              :            46195
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 101                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    4.41
 p-value of test no 102                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.27
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.66
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.73
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.69
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.98
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.64
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.06
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.50
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.71
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.45
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.92
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17221.63
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.50
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.23
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.69
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.08
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.78
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.63
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.02
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.48
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.90
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.44
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.54
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.62
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.96
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.47
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.37
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.14
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.75
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  177.95
 p-value of test no 164                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.86
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.76
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.43
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.23
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.86
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.05
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.98
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.44
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.71
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.44
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.63
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.95
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.50
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.77
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-3
 p-value of test no 190                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.39
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.06
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.96
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.25
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.28
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.48
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5021.27
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.68
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4207.13
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.74
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.52
 p-value of test no 229                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.99
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.90
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000145447
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.37
 p-value of test no 233                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000008764
 
 Normal statistic for number of bits   :   0.069
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.31
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 251                :    0.9980
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.61
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:01.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35635
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 6                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5495
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7586
 p-value of test no 21                 :  9.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    3.23
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.96
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 30                 :    0.9974
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 32                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.79
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 47                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.41
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.03
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.81
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.16
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.31
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.28
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.02
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.88
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.04
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6996.55
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
 p-value of test no 59                 :    0.9928
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.66
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.96
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.14
 p-value of test no 66                 :  4.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  147.51
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4931.49
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46379
 p-value of test no 70                 :  1.0e-2
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870379
   j =  1                              :        399907247
   j =  2                              :            46369
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46035
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870035
   j =  1                              :        399907933
   j =  2                              :            46029
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.92
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.47
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.22
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.36
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.56
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.30
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.55
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.47
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.00
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.73
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17723.66
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.09
 p-value of test no 146                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.49
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.13
 p-value of test no 148                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.72
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.37
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.94
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.11
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.12
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.12
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.76
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.92
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.43
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.49
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.14
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.91
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.39
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.94
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.03
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.69
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.30
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.76
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.22
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.58
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.76
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.42
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.35
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.20
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.41
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.25
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.90
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.20
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.39
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 183                :    0.86
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 188                :    0.53
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.66
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.19
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.55
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.48
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.12
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 216                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 218                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.73
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.32
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.66
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.01
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.75
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.24
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.47
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999954104
 
 Normal statistic for number of bits   :   -0.36
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.36
 p-value of test no 233                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999865163
 
 Normal statistic for number of bits   :   -1.07
 p-value of test no 234                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 237                :    0.9976
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.94
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    2.41
 p-value of test no 249                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:57.70
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        9.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35636
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 6                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 9                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 18                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.42
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.59
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.80
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.82
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.81
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.51
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.19
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.83
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.62
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.94
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.52
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.13
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.24
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.97
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4916.78
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45630
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869630
   j =  1                              :        399908742
   j =  2                              :            45626
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45462
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869462
   j =  1                              :        399909079
   j =  2                              :            45456
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
 p-value of test no 84                 :    0.9950
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.071
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.33
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.99
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.36
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.85
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.98
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.41
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.82
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-3
 p-value of test no 142                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17911.62
 p-value of test no 145                :  5.2e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.59
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.36
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.82
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.71
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.03
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.88
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.17
 p-value of test no 153                :    0.9921
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.85
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.13
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.85
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.25
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.71
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.95
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.36
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.88
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.54
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.02
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.21
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.78
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.00
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.80
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.61
 p-value of test no 169                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.32
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.86
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.95
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4763.47
 p-value of test no 173                :    0.9917
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.74
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.11
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.88
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.19
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 183                :    0.85
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.065
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.09
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.10
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.64
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.75
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.89
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 221                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4779.98
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.90
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3908.78
 p-value of test no 227                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.01
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11950.62
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.80
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.87
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999881258
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.28
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999931847
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:00.48
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35637
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 4                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 11                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 19                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 23                 :    0.9967
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.58
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.31
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.75
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.21
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.04
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.27
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.78
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  504.94
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.17
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7173.70
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.23
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.47
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.16
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.74
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.47
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46229
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870229
   j =  1                              :        399907546
   j =  2                              :            46221
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908661
   j =  2                              :            45662
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    4.11
 p-value of test no 74                 :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 102                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.85
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.81
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.46
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.12
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.50
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.58
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.42
 p-value of test no 129                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.66
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.42
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.14
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.34
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.33
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.40
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.21
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.47
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.80
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.12
 p-value of test no 152                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.04
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.66
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.19
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.63
 p-value of test no 156                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.96
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.33
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.20
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.97
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.08
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.73
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.44
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.88
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.49
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.44
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4889.92
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.62
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.53
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.81
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.96
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.63
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.23
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.88
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.48
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.58
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.29
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.50
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.24
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.31
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.76
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10023.46
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4842.04
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.60
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.97
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.81
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.43
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.53
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.17
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000103078
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.19
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000103189
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.57
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:08.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35638
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    2.09
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 44                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.38
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.79
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.99
 p-value of test no 49                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.55
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.69
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.79
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.81
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.97
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.96
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7065.70
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.39
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.16
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.91
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.88
 p-value of test no 67                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5102.46
 p-value of test no 68                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908475
   j =  2                              :            45761
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45873
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869873
   j =  1                              :        399908255
   j =  2                              :            45871
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 107                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.33e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.96
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.16
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.40
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.67
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.34
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.05
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.78
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.00
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.92
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17665.60
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.78
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.48
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.44
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.21
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.95
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.72
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.59
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.19
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.95
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.83
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.82
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  189.50
 p-value of test no 159                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.77
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.71
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.06
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.47
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.08
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.74
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.93
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.17
 p-value of test no 167                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.63
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.94
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.59
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.28
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.59
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4811.70
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.69
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.80
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.98
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.54
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.98
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.21
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.22
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9982.18
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.20
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 224                :  7.3e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.07
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.52
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.22
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11895.59
 p-value of test no 229                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.35
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.40
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999936479
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.52
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000107710
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.74
 p-value of test no 248                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.28
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:17.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35639
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5472
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.38
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.15
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.68
 p-value of test no 48                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.81
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.17
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.01
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.11
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.13
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.63
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.39
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.13
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7260.54
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.45
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.45
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.32
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.28
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5173.67
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45764
 p-value of test no 70                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869764
   j =  1                              :        399908475
   j =  2                              :            45758
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45685
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869685
   j =  1                              :        399908631
   j =  2                              :            45683
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.28
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.59
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.11
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.84
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.24
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.29
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.76
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.44
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.03
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17215.12
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.13
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.36
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.89
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.86
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.54
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.91
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.02
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.30
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.32
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.73
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.79
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.58
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.70
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.63
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  108.38
 p-value of test no 160                :  5.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   91.62
 p-value of test no 161                :    0.9999    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.72
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.14
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.84
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.30
 p-value of test no 165                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.01
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.73
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.35
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.16
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.34
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.75
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.80
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5069.80
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.27
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.13
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.78
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.13
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.97
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.77
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.66
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9813.86
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.75
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.011
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.02
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.68
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.14
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.00
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.00
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.88
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.15
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999842183
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   34.09
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000064870
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 238                :    0.59
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 241                :    0.99
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.28
 p-value of test no 248                :    0.99
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:32.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35640
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    2.89
 p-value of test no 33                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.08
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.42
 p-value of test no 40                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.67
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.13
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.74
 p-value of test no 49                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.60
 p-value of test no 51                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.94
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.71
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.01
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.48
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.14
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.26
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.49
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.78
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.03
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4995.61
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908091
   j =  2                              :            45953
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45781
 p-value of test no 71                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869781
   j =  1                              :        399908444
   j =  2                              :            45769
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.017
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.74
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.33
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.53
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.54
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.61
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.44
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.85
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.20
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.10
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.06
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.25
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.42
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17299.10
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.82
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.94
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.33
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.40
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.67
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.31
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.63
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.17
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.48
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.18
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.67
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.33
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.14
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.80
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.71
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.49
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.61
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.71
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.11
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.82
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.10
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.82
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.64
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.67
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.73
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.48
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.93
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.65
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.09
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.01
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.07
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.01
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.07
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.58
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.53
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10235.51
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.35
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 217                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.52
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.15
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.69
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.29
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.20
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.31
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.90
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999881768
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.11
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999918575
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9970
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    1.60
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:52.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35641
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 7                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 15                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7459
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 21                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.13
 p-value of test no 28                 :    0.9995    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 38                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.00
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.49
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.30
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.18
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.92
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.54
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  198.80
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.68
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.13
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.63
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.10
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
 p-value of test no 63                 :    0.9973
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.44
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.70
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.55
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.59
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907926
   j =  2                              :            46028
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.94
 p-value of test no 116                : 1 -  4.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.47
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.74
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.42
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.14
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.13
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.47
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.78
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.80
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.13
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17520.68
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.50
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.00
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.48
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.16
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.03
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.01
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.61
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.84
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.40
 p-value of test no 155                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.07
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.61
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.45
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   91.84
 p-value of test no 159                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.79
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.47
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.88
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.16
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.96
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.38
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.14
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.82
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.19
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.43
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.26
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.20
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.12
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.08
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.52
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.01
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.60
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.42
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.05
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.49
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
 p-value of test no 205                :    0.9903
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.21
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.94
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.13
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.40
 p-value of test no 217                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.097
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.78
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 3.60e-3
 p-value of test no 224                :    0.9963
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4684.11
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.51
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.33
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11586.06
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.05
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.02
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000164149
 
 Normal statistic for number of bits   :    1.30
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.71
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000108097
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.95
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 243                :    0.79
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 7.36e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 253                :    0.97
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:21.15
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            0.9995 
  56  SampleCorr, k = 2              1 -  4.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35642
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1247
 p-value of test no 11                 :    0.9993    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334367
   j =  1                              :        599997506
   j =  2                              :             1247
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5389
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     871
 p-value of test no 25                 :    0.83
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    2.35
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 46                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.00
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.08
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.16
 p-value of test no 50                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.33
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.08
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.65
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.82
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.54
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.32
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6873.85
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.20
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 64                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.51
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.47
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.01
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.65
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908364
   j =  2                              :            45818
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45466
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869466
   j =  1                              :        399909071
   j =  2                              :            45460
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.95
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.62
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.10
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.23
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.06
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.05
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.39
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.96
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.09
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.66
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.56
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.87
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.48
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.97
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.27
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.37
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.27
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.39
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.73
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.17
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.22
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.89
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.09
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.73
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.61
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.05
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.10
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.67
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.81
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.98
 p-value of test no 166                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.15
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.21
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.60
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.77
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.19
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.15
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5243.77
 p-value of test no 173                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.71
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.90
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.23
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.88
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
 p-value of test no 191                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.24
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.47
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.65
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10067.27
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 214                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.30
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.39
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 225                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.70
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.63
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.80
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11739.65
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.05
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.25
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999935177
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.81
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999914354
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 246                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.92
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:01.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35643
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5433
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.34
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    2.85
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    2.56
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.31
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.90
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.14
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.04
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.58
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.26
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.60
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.62
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.60
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.70
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.05
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7244.49
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.82
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.43
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.39
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.20
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5218.38
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45674
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869674
   j =  1                              :        399908655
   j =  2                              :            45668
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908409
   j =  2                              :            45791
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.06
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.71
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.65
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.31
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.47
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.38
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.77
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 132                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.38
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.46
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.65
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.87
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.06
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.11
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.93
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.21
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.60
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.37
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.99
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.06
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.26
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.71
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.34
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.85
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.54
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.07
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  167.70
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.53
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.79
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.68
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.17
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.04
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.35
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.26
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.22
 p-value of test no 172                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5222.26
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.36
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.32
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.32
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.58
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.87
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.73
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.29
 p-value of test no 196                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.33
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 201                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.28
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.01
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.15
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.34
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.88
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  3.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 225                :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4645.44
 p-value of test no 226                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.64
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.13
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.86
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.38
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.23
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999947912
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.18
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000011959
 
 Normal statistic for number of bits   :   0.095
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 238                :    0.26
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 243                :    0.91
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.64
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.67
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35644
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 12                 :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7020
 p-value of test no 18                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.97
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.32
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.49
 p-value of test no 46                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.46
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.27
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.76
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.58
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.47
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.76
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.37
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.92
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.60
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.04
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.72
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.91
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.61
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.84
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.77
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908401
   j =  2                              :            45798
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908200
   j =  2                              :            45897
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 76                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.23
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.08
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.06
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.37
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.82
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.79
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.83
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.31
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17332.28
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.14
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.11
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.12
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.96
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.52
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.72
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.07
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.53
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.24
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.94
 p-value of test no 156                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.40
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.94
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.99
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.63
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.64
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.02
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.42
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.54
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.84
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.44
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.44
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.66
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.86
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.93
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.49
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.91
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.73
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.38
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.39
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.12
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.66
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.61
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 188                :    0.26
 
 Sample variance                       :    2.57
 p-value of test no 189                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.01
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.20
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.71
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.79
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9928.40
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.044
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4865.27
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5096.68
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3945.09
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.69
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.79
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.45
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.83
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000128473
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.91
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999931406
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.79
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.070
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:24.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35645
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 6                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1466
 p-value of test no 11                 :  3.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334586
   j =  1                              :        599997068
   j =  2                              :             1466
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5626
 p-value of test no 13                 :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4431
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 30                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     665
 p-value of test no 31                 :  4.7e-3
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.04
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.67
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.99
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.27
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.26
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.95
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.80
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  390.20
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.65
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7106.43
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.51
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.86
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.48
 p-value of test no 67                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4949.79
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907762
   j =  2                              :            46113
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45736
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869736
   j =  1                              :        399908530
   j =  2                              :            45732
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.48
 p-value of test no 115                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.54
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.84
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.39
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.10
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.80
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.76
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.48
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 130                :  1.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 132                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.15
 p-value of test no 133                :    0.9901
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.62
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.55
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17124.54
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.34
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.52
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.00
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.06
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.62
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.91
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.19
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.22
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.79
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.15
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.22
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.94
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.22
 p-value of test no 160                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.71
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.24
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.82
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.54
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.58
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.54
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.45
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.08
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.10
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.42
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.02
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.45
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5171.48
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.35
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.94
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.62
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.86
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.69
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.30
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.47
 p-value of test no 207                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.73
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.31
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 220                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.31
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.65
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.37
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.47
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.77
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.01
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.94
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999906584
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.03
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999970112
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 237                :    0.9983
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.61
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35646
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4499
 p-value of test no 14                 :  7.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    2.12
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.12
 p-value of test no 30                 :    0.9998    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.80
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.41
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.05
 p-value of test no 50                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.43
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.19
 p-value of test no 52                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.29
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.61
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  503.04
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.00
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7211.34
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.41
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.93
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.56
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.65
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.61
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908237
   j =  2                              :            45877
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45474
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869474
   j =  1                              :        399909055
   j =  2                              :            45468
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 3.38e-6
 p-value of test no 113                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.49
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.89
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.61
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.30
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.60
 p-value of test no 123                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.97
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.82
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.81
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.43
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 134                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.75
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.01
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17311.01
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.97
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.29
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.41
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.43
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.33
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.26
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.42
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.65
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.31
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.28
 p-value of test no 157                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.97
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.00
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.24
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.00
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.34
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.58
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.84
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.52
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.09
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5127.79
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  339.99
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.54
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.28
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.06
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.49
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.75
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.27
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.41
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.48
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.58
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.75
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.39
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10179.26
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.66
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.01
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.02
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.63
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.77
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.72
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.57
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.40
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  7999917618
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.30
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000029443
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.37
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.067
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 248                :    0.07
 
 Sample variance                       :    2.24
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 253                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:47.67
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35647
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 11                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7565
 p-value of test no 18                 :  2.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.83
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    2.25
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.24
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.96
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.47
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.67
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.27
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.12
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.37
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.20
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.77
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.18
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.28
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.51
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.36
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.59
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.03
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908478
   j =  2                              :            45755
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45668
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869668
   j =  1                              :        399908666
   j =  2                              :            45664
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 86                 :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 3.87e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 116                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.78
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.92
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.10
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.97
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.00
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.63
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.12
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.92
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.59
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 139                :  4.5e-3
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 140                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.36
 p-value of test no 141                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.64
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.93
 p-value of test no 146                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.78
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.07
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.49
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.67
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.41
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.95
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.21
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.54
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.33
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.35
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.62
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.33
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.65
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.43
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.44
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.19
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.60
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.78
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.64
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.69
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.05
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.61
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.48
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.37
 p-value of test no 170                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.65
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.06
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.21
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.00
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.89
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.29
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.04
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.30
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.38
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
 p-value of test no 185                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.39
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 202                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.53
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.63
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.71
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9775.71
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.70
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.16
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.74
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4225.06
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11414.77
 p-value of test no 229                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11875.59
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.24
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999886226
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.02
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999959156
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 243                :    0.39
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:25.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35648
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 12                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    2.46
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.23
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.05
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.62
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.57
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.50
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.24
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.06
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.42
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.09
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.04
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.24
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7117.86
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.18
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 64                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.10
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.95
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.90
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.09
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908236
   j =  2                              :            45876
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45676
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869676
   j =  1                              :        399908648
   j =  2                              :            45676
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
 p-value of test no 103                :    0.9967
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 105                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.37e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 116                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.35
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.02
 p-value of test no 120                :  4.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.28
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.90
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.51
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.31
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.19
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.06
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.33
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.75
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.03
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.47
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.15
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.03
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.27
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.79
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.12
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.76
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.49
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.90
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.18
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.13
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.60
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.91
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.61
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.14
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.60
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.41
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.79
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.82
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.64
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.92
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  435.61
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.17
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.17
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.35
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5103.09
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.24
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.07
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.80
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.14
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.76
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.83
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.24
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.35
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10258.34
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.96
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.85
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.16
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.12
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.91
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.22
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.44
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.64
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000024451
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.86
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999959225
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.051
 p-value of test no 253                :    0.52
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:28.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35649
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 9                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5490
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 20                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.86
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.17
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.89
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.14
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.76
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.33
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1358.71
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7319.46
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.12
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.10
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.93
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.36
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908736
   j =  2                              :            45626
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908081
   j =  2                              :            45955
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.68
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.52
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.29
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.40
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.29
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.73
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.40
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.27
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.82
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17405.70
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.29
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.45
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.67
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.82
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.47
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.78
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.80
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.39
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.39
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.94
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.00
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.69
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.94
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.87
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.35
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.36
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.85
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.07
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.95
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.10
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.04
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.76
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.26
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.67
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.81
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.77
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.74
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.27
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.44
 p-value of test no 196                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.20
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.51
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.99
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 210                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10359.08
 p-value of test no 211                :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10176.03
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.11
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.38
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4074.61
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.25
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.28
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.80
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.37
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000006712
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.15
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000018367
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.054
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35650
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 6                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 10                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.51
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.06
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.25
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.07
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.98
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.36
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.86
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.71
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1363.01
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7160.03
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.93
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.35
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.39
 p-value of test no 66                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.86
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5155.51
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908492
   j =  2                              :            45748
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45660
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869660
   j =  1                              :        399908682
   j =  2                              :            45656
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 78                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.85e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.40
 p-value of test no 116                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.49
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.22
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.51
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.28
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.90
 p-value of test no 124                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.39
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.12
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.92
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
 p-value of test no 139                :    0.9964
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.52
 p-value of test no 141                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17189.28
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.60
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.22
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.12
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.19
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.52
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.30
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.45
 p-value of test no 153                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.55
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.93
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.84
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.88
 p-value of test no 157                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.93
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.02
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.94
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.40
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.87
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.92
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.40
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.27
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.99
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.17
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.95
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.99
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  162.38
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.51
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.91
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.30
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.13
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.99
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 177                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.72
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.91
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.16
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.71
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.66
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.85
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10058.13
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.40
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.61
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.07
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.61
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.27
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.05
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.51
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.69
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.29
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999889121
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.74
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000045571
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 248                :    0.85
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:31.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35651
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 10                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997139
   j =  2                              :             1426
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.25
 p-value of test no 46                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.94
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.02
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.69
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.90
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 51                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.90
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.05
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.45
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.95
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.78
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.00
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.17
 p-value of test no 61                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.84
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.14
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4963.06
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908629
   j =  2                              :            45681
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 88                 :    0.9995    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 117                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.58
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.85
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.71
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.51
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.03
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.56
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.52
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.02
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.40
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.39
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 137                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.82
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.17
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.87
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.87
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.56
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 149                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.59
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.72
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.18
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.88
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.21
 p-value of test no 154                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.97
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.77
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.63
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.70
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.31
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.87
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.12
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.38
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  582.07
 p-value of test no 163                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.52
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.27
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.22
 p-value of test no 166                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.54
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5061.86
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.49
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.68
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.18
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.51
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.18
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.80
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.80
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.80
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.079
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 183                :    0.69
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.57
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.66
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 205                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.01
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.13
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.98
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.081
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.31
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.65
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.99
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.06
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.68
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.75
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.63
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999980057
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000040006
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:07.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35652
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4208
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.49
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.56
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.25
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.87
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.28
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.31
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.74
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.87
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.66
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7233.49
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.83
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.90
 p-value of test no 65                 :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.40
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.01
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907879
   j =  2                              :            46056
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908486
   j =  2                              :            45751
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 95                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 98                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 107                :    0.03
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 117                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.62
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.89
 p-value of test no 120                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.70
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.58
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.61
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.93
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   55.97
 p-value of test no 125                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.71
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.98
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.69
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.11
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.78
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17634.21
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.63
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.36
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.63
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.34
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.84
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.74
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.40
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.12
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.93
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.96
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.02
 p-value of test no 157                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.32
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.66
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.90
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.56
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.09
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.01
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.62
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.60
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.20
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.00
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.70
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.13
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.29
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.24
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5090.79
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.78
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  274.27
 p-value of test no 175                :  3.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.23
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.63
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 183                :    0.78
 
 Sample variance                       :    0.40
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.64
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.47
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.37
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.24
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.16
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10166.52
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.73
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.63
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.61
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.50
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.08
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.58
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.06
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999902279
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.01
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999999686
 
 Normal statistic for number of bits   : -2.48e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 238                :    0.31
 
 Sample variance                       :    2.64
 p-value of test no 239                :  4.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.30
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    2.02
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 C (L=10000, r=15)   3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35653
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 11                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5388
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7544
 p-value of test no 19                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.62
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.63
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.06
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.03
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.19
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.92
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.80
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.38
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.25
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1516.78
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6883.65
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.29
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.35
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.78
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.19
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.09
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45571
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869571
   j =  1                              :        399908863
   j =  2                              :            45561
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908633
   j =  2                              :            45673
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 85                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-5
 p-value of test no 112                :    0.9920
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-4
 p-value of test no 113                :    0.01
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 114                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 115                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.61
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.99
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.56
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.40
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.06
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.51
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.97
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.16
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.44
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.38
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.91
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.88
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.63
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.23
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.92
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.63
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.17
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.69
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.37
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.70
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.65
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.52
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.35
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.20
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.87
 p-value of test no 160                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.92
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.81
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.61
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.99
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.70
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.44
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.26
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.26
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.43
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.79
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.15
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.92
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4968.92
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.25
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.40
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.67
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.70
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.00
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.26
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.12
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.04
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 212                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10188.56
 p-value of test no 215                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.13
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.43
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.77
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.80
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.80
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12094.48
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.51
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999876512
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.14
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000006715
 
 Normal statistic for number of bits   :   0.053
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.92
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 243                :    0.21
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 248                :    0.13
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:20.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35654
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5299
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7455
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.58
 p-value of test no 23                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 28                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.83
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.25
 p-value of test no 47                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.61
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.76
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.02
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.60
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 52                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.27
 p-value of test no 53                 :    0.9944
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.08
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.37
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.07
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.73
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.04
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.16
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.66
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.01
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908124
   j =  2                              :            45938
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907920
   j =  2                              :            46031
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 78                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
 p-value of test no 109                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 8.85e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.013
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.60
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.86
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.64
 p-value of test no 121                :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.02
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.45
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.21
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.93
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.44
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17452.67
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.92
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.83
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.01
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.79
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.51
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.01
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.93
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.39
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.11
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.40
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.67
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.18
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.48
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.45
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.85
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.38
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.73
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.69
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.80
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.65
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4923.15
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.91
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.31
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.66
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.63
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.62
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.51
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.94
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.14
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.46
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.76
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.11
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.55
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.80
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.47
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.53
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.020
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 221                :    0.9904
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.49
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4947.65
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.92
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.86
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11755.92
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.83
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.34
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000054964
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.71
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  8000021619
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.82
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:28.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35655
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.37
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.80
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.49
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.30
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.01
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.75
 p-value of test no 50                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.86
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.38
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.15
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.93
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.67
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.65
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.56
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.54
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.19
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.60
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.42
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5061.75
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907734
   j =  2                              :            46130
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908233
   j =  2                              :            45879
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 73                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 105                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.99e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-5
 p-value of test no 112                :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 115                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.033
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.91
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.01
 p-value of test no 121                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.99
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.24
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.28
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 128                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.01
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.02
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.96
 p-value of test no 135                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.18
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17426.13
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.83
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.68
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.09
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.69
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.98
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.78
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.08
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.68
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.03
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.08
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.13
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.88
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.42
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.24
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.35
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.02
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.84
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.92
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.03
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.11
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.85
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.35
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.49
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.86
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.94
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.14
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.87
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.62
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.82
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.05
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.23
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 188                :    0.06
 
 Sample variance                       :    1.73
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.86
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.84
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 200                :  4.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.15
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 204                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.85
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.43
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10208.30
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 216                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.38
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.11
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3920.70
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3968.78
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11763.90
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11670.05
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.16
 p-value of test no 231                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000133528
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.33
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000018622
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 243                :    0.15
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 248                :    0.03
 
 Sample variance                       :    2.74
 p-value of test no 249                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    1.62
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:40.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35656
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 4                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 5                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 10                 :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.27
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.69
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.71
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.86
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.11
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.72
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.92
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.65
 p-value of test no 55                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.70
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6812.38
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.37
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.49
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.16
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.88
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.32
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45551
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869551
   j =  1                              :        399908902
   j =  2                              :            45543
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46149
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870149
   j =  1                              :        399907705
   j =  2                              :            46143
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.40e-4
 p-value of test no 109                :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 113                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.52
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.22
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.38
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.81
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.89
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.81
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.91
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.65
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.14
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.42
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17399.98
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.93
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.51
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.96
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.28
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.95
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.02
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.44
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.06
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.95
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.27
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.45
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.16
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.18
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.58
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.02
 p-value of test no 160                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.98
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.09
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.02
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.52
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  454.27
 p-value of test no 166                :  7.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.11
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.41
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.40
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.55
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.62
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.92
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.86
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.56
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.81
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.86
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 183                :    0.42
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.39
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.14
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.86
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.47
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10002.29
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9991.03
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.92e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4815.72
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.31
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.26
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4331.05
 p-value of test no 228                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11582.20
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.55
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.46
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999861227
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.94
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000026590
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 247                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35657
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 5                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 6                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5487
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.36
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 44                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.07
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.91
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.49
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.39
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.06
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.33
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.72
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1428.52
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.61
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.60
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.90
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.58
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.48
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.98
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 70                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908220
   j =  2                              :            45887
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908426
   j =  2                              :            45781
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.06
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9908
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 84                 :    0.9905
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.28
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.26
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.84
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.35
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.97
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.52
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.91
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.70
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.32
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.06
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.01
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.10
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.92
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.28
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.00
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.21
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.31
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.54
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.34
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.83
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.52
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.69
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.74
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.75
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.45
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.56
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.74
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.74
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.13
 p-value of test no 165                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.12
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.02
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.33
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.17
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.63
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.91
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.24
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.00
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.63
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.21
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.05
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.97
 p-value of test no 178                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.21
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.36
 p-value of test no 183                :    0.91
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.14
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.17
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 198                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.07
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 206                :    0.9919
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.69
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.53
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10327.94
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 218                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.39
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.98
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3926.77
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4334.47
 p-value of test no 228                :  9.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.16
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.57
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.70
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999914900
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.29
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999957044
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.37
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:58.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35658
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 12                 :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7612
 p-value of test no 15                 :  3.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 26                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 29                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.02
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.56
 p-value of test no 49                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.62
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.89
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.28
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.93
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  414.00
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.18
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.68
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.62
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.42
 p-value of test no 65                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.91
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.82
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.71
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908020
   j =  2                              :            45981
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45868
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869868
   j =  1                              :        399908266
   j =  2                              :            45864
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 107                :    0.9910
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.59
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.16
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.16
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.30
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.71
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.11
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.23
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.04
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.82
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.06
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17496.95
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.92
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.49
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.02
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.59
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.35
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.09
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.02
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.72
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.94
 p-value of test no 156                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.02
 p-value of test no 157                :  5.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.84
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.14
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.09
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.38
 p-value of test no 161                :    0.9943
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.28
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.06
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.40
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.33
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.51
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.62
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.12
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.39
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.93
 p-value of test no 170                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.60
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.86
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.41
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.25
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.81
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.58
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.37
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.02
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.32
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.13
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.32
 p-value of test no 203                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.31
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.41
 p-value of test no 211                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9972.62
 p-value of test no 215                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5086.36
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4945.67
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4327.53
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.35
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.51
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11626.04
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.52
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000072004
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.23
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000023977
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.37
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.75
 p-value of test no 244                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 248                :    0.74
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 253                :    0.26
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:42.57
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  15  BirthdaySpacings, t = 4         3.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35659
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5424
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4180
 p-value of test no 14                 :    0.9915
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.17
 p-value of test no 23                 :    0.9966
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.59
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.94
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.32
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.33
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.00
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.77
 p-value of test no 54                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.68
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.96
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.79
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.59
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.15
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.49
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.12
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.48
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908427
   j =  2                              :            45779
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907966
   j =  2                              :            46011
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 94                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 101                :    0.9939
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.69
 p-value of test no 115                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.75
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.59
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.01
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.98
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.57
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.70
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.63
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.08
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.19
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.35
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.95
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.06
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.73
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.71
 p-value of test no 148                :  5.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.11
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.05
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.42
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.70
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.84
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.19
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.87
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.59
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.90
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.19
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.69
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.23
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.49
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.63
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.15
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.66
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.01
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.86
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.03
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.62
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.01
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.17
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.14
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.73
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.35
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.21
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.04
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.49
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 187                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.55
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
 p-value of test no 190                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.89
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.31
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 206                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.85
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9830.74
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.35
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 220                :    0.02
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5035.68
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.25
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.09
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.79
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.88
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11664.82
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.74
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999923795
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.63
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000134383
 
 Normal statistic for number of bits   :    1.06
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.19
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.18
 p-value of test no 244                :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 253                :    0.62
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35660
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 4                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5344
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     844
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 32                 :    0.9988
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.98
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.94
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.89
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.56
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.92
 p-value of test no 48                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.16
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.02
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.19
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.42
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.96
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.95
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.60
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.92
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.49
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.35
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.49
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.74
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  151.45
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.66
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45546
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869546
   j =  1                              :        399908911
   j =  2                              :            45540
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908589
   j =  2                              :            45701
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.87e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.50
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.92
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.65
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.89
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.65
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.38
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.46
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.34
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17310.89
 p-value of test no 145                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.42
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.47
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.46
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.98
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.91
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.47
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.91
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.33
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.30
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    4.93
 p-value of test no 155                :    0.9980
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.04
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.69
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.85
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.78
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.12
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.61
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.20
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.43
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.87
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.45
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.22
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.39
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.41
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.84
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.10
 p-value of test no 171                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.40
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4945.12
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.04
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.63
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.36
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.33
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.49
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.18
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.51
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.04
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10041.27
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.45
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4949.08
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.02
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.15
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4240.16
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12133.22
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12134.97
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.11
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999969101
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.81
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999946085
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 238                :    0.96
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:26.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35661
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 3                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1260
 p-value of test no 6                  :    0.9978
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334380
   j =  1                              :        599997480
   j =  2                              :             1260
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 17                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.18
 p-value of test no 22                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.00
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.90
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.94
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.51
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.98
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.20
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.73
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.68
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  181.24
 p-value of test no 54                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.04
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.64
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.68
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.19
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.3e-3
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.73
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.75
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.49
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.70
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45546
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869546
   j =  1                              :        399908912
   j =  2                              :            45538
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908239
   j =  2                              :            45876
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 102                :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.89
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.95
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.39
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.60
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.60
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.87
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.84
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.52
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.70
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.51
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.21
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.49
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.11
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.08
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.44
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.83
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.84
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.60
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.72
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.68
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.60
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.83
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.20
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.55
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.52
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.57
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.26
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.42
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.26
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.22
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.16
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.87
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.52
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.85
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.86
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4906.12
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.30
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.70
 p-value of test no 175                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.71
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.42
 p-value of test no 177                :    0.9922
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.83
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.88
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.39
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 205                :  7.2e-3
 
 Anderson-Darling statistic = A2       :    6.01
 p-value of test no 206                :  1.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  272.67
 p-value of test no 207                :  4.8e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.28
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9945.31
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.69
 p-value of test no 216                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.97
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.40
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.61
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.08
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11882.09
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.58
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.05
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999946205
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.55
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999849560
 
 Normal statistic for number of bits   :   -1.19
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 238                :    0.38
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.50
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:19.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        4.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35662
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5306
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.75
 p-value of test no 22                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 23                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    2.23
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.09
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.42
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 41                 :    0.9947
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.35
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.94
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.57
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.94
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.04
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.36
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.66
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.66
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.14
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.41
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.16
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.81
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.90
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.47
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46113
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870113
   j =  1                              :        399907777
   j =  2                              :            46107
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46203
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870203
   j =  1                              :        399907596
   j =  2                              :            46199
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 104                :  3.8e-3
 
 Anderson-Darling statistic = A2       :    3.45
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-6
 p-value of test no 110                :    0.9966
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.091
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.00
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.03
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.68
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.32
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.95
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.14
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.15
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.28
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9928
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.67
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.60
 p-value of test no 137                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.13
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17668.44
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.31
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.41
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.53
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.14
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.38
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.84
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.65
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.61
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.88
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.07
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.05
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.32
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.95
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.50
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.60
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.34
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.92
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.47
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.10
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.33
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.31
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.59
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.50
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.98
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.00
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.12
 p-value of test no 171                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.92
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.27
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.15
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.97
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 183                :    0.96
 
 Sample variance                       :    2.31
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 188                :    0.72
 
 Sample variance                       :    2.13
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.91
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.62
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.91
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.57
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10157.96
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.02
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.80
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.89
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.07
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.85
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.06
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.91
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000113338
 
 Normal statistic for number of bits   :    0.90
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999961379
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.95
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:35.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35663
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5460
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    4.33
 p-value of test no 42                 :  6.0e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     176
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.93
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.48
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.70
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.61
 p-value of test no 49                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.72
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.81
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.40
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.72
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.45
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.45
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.51
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.37
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.86
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.33
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.60
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5181.52
 p-value of test no 68                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908411
   j =  2                              :            45787
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907839
   j =  2                              :            46070
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.10
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.97
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.25
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.98
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.32
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.59
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-3
 p-value of test no 131                :    0.9978
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.42
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.32
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17711.88
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.58
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.48
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.51
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.93
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.59
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.58
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.90
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.44
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.47
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.12
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.32
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.69
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.50
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.38
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.16
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.55
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.43
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.16
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.97
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.25
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.85
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.29
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.57
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.50
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.42
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.59
 p-value of test no 171                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.30
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.82
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.87
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.43
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.87
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.88
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.17
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.14
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.23
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.06
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.25
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9819.32
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.68
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.10
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.11
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.59
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11660.37
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.06
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.47
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999982481
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.68
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000030265
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.38
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:26.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35664
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 3                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5325
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 19                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 29                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 34                 :    0.9985
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.35
 p-value of test no 40                 :  6.5e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.71
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.68
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   95.57
 p-value of test no 51                 :  4.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.57
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.03
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.86
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.67
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.73
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.20
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.26
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 63                 :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.07
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.13
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.54
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4913.69
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908570
   j =  2                              :            45712
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46075
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870075
   j =  1                              :        399907854
   j =  2                              :            46067
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 104                :    0.02
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.99
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.94
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.39
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.76
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.58
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.90
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.88
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.88
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 131                :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.54
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.49
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   96.50
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.23
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.07
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.11
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.41
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.50
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.36
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.21
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.35
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   43.63
 p-value of test no 153                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.33
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    3.92
 p-value of test no 155                :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.13
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.46
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.70
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.17
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.45
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.09
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.75
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  529.61
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.53
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.55
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.70
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.22
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.92
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.12
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.10
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.21
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.24
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4744.81
 p-value of test no 173                :    0.9952
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.28
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.03
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.73
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.48
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.54
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9949
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 3.12e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.85
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.11
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.41
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.61
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.53
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.42
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.37
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.50
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.09
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.03
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.38
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.90
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12125.72
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.06
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000066022
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999959108
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:04.46
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  31  CouponCollector, r = 10         4.2e-4
  75  RandomWalk1 C (L=50, r=25)      0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35665
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 11                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    2.57
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     542
 p-value of test no 31                 :    0.9913
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.12
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.68
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.00
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.93
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.38
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.17
 p-value of test no 52                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.98
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.07
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.94
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.80
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.15
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.55
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.69
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.12
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.26
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.36
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45899
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869899
   j =  1                              :        399908204
   j =  2                              :            45895
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908553
   j =  2                              :            45719
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-4
 p-value of test no 72                 :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 98                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 100                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
 p-value of test no 113                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.06
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.86
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.96
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.38
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.45
 p-value of test no 123                :    0.9953
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.58
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.64
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.32
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.59
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.17
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.45
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17348.60
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.43
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.99
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   53.72
 p-value of test no 148                :  7.2e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.72
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.06
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.97
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.46
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.46
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.94
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.23
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.50
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.56
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.68
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.56
 p-value of test no 160                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.44
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.02
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.92
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.50
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.34
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.71
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.75
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5083.70
 p-value of test no 168                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.71
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.06
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.61
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.16
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5292.49
 p-value of test no 173                :  2.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.36
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.20
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.83
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.14
 p-value of test no 178                :    0.9945
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 188                :    0.19
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 195                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.95
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.89
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.29
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9795.88
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 214                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.64
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.76e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.28
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.12
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.37
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.92
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.99
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.39
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.45
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000081442
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999924293
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:58.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       7.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35666
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 6                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 7                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5522
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    2.67
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9916
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.99
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.45
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.60
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.56
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.17
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.07
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.74
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.14
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.43
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.40
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.87
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.71
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4923.61
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908089
   j =  2                              :            45951
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908847
   j =  2                              :            45575
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 78                 :    0.9916
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.64e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.63
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.95
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.05
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.27
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.49
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.17
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.30
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.75
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.89
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.39
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.45
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17726.29
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.20
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.56
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.66
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.43
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.92
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.06
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.64
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.15
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.21
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.26
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.83
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.59
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.57
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.77
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.62
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.86
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.12
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.72
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.50
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.79
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.97
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.83
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.00
 p-value of test no 168                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.27
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.27
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.18
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.35
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.07
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.04
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.98
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.98
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.23
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.79
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.21
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.47
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.85
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.00
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.28
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4742.80
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.31
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4198.40
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.38
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12010.95
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.07
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999876353
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.01
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999877004
 
 Normal statistic for number of bits   :   -0.97
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.75
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 253                :    0.20
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:46.01
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35667
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     126
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.85
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.83
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.99
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.41
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.03
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.88
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.23
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   28.90
 p-value of test no 53                 :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.06
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.24
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.12
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.41
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.40
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.34
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.11
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4860.42
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46105
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870105
   j =  1                              :        399907792
   j =  2                              :            46101
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46010
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870010
   j =  1                              :        399907987
   j =  2                              :            45996
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
 p-value of test no 110                :    0.95
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.91
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.35
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.13
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.63
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.29
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.82
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.87
 p-value of test no 125                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.92
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.68
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.79
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17516.41
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.03
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.75
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.93
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.01
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.37
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.39
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.14
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.09
 p-value of test no 155                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.82
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.07
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.71
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.99
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.16
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.56
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.90
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.74
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.63
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.96
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.22
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.99
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.34
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.37
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.15
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.17
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.37
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  332.90
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.74
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.76
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.44
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.02
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.84
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.55
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.76
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.16
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.03
 p-value of test no 211                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.32
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.12
 p-value of test no 217                :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.73
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 225                :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.35
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.74
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4034.71
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.32
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.62
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.13
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000093640
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.69
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000036181
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.10
 p-value of test no 254                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:18.96
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35668
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 14                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7535
 p-value of test no 15                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7546
 p-value of test no 21                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 40                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 42                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 44                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.79
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.21
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.70
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.43
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.53
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.92
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.57
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.68
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.93
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.51
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.28
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.69
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.08
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.82
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.69
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.54
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46285
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870285
   j =  1                              :        399907433
   j =  2                              :            46279
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45680
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869680
   j =  1                              :        399908644
   j =  2                              :            45672
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 97                 :  1.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    7.21
 p-value of test no 99                 :  2.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.68
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.97
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.08
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.08
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.48
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.65
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.10
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.26
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.47
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.70
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.87
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.38
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.93
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.10
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.37
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.31
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.13
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.33
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.90
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.69
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.59
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   95.13
 p-value of test no 156                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.72
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.71
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.46
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.89
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.27
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.81
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.07
 p-value of test no 163                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.58
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.14
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  459.90
 p-value of test no 166                :  4.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.46
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.51
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.74
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.10
 p-value of test no 170                :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.68
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.42
 p-value of test no 172                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.35
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  314.00
 p-value of test no 174                :    0.9928
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.51
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.58
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.82
 p-value of test no 178                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.23
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.12
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.99
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.11
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.93
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.64
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.26
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4933.40
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.35
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.35
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.42
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11685.90
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11623.63
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999955139
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.63
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000048163
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.14
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    1.92
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.92e-3
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -6.02e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:31.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               2.8e-4
  76  RandomWalk1 H (L=1000, r=0)     0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35669
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 9                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5401
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.43
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    2.60
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 40                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.60
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.00
 p-value of test no 47                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.15
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.24
 p-value of test no 49                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.23
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.98
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.07
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.76
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.23
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.61
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.91
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.29
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.00
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.55
 p-value of test no 65                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.39
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.99
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5100.91
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45780
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869780
   j =  1                              :        399908441
   j =  2                              :            45778
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908637
   j =  2                              :            45674
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 105                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
 p-value of test no 113                :    0.02
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.19
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.49
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.80
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.67
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.12
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.75
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.36
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.66
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 143                :  6.0e-3
 
 Anderson-Darling statistic = A2       :    4.78
 p-value of test no 144                :  3.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17988.83
 p-value of test no 145                :  1.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.38
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.36
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.81
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.49
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.52
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.20
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.74
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.44
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.19
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.88
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.91
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.71
 p-value of test no 158                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.54
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.72
 p-value of test no 160                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.01
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.83
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.72
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.78
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.52
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.07
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.28
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4901.39
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.22
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.35
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.20
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.43
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.75
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.70
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.81
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.03
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.33
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.22
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-4
 p-value of test no 186                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 187                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.55
 p-value of test no 188                :    0.9947
 
 Sample variance                       :    1.47
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.90
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.13
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.65
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10004.34
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.14
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.19
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.48
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.56
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.03
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.93
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.90
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.18
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  8000149557
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 232                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.59
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999972305
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.79
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 248                :    0.38
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 4.64e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:47.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35670
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 17                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.76
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.18
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.83
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.02
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.27
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.65
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.87
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.16
 p-value of test no 52                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.97
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  178.04
 p-value of test no 54                 :    0.9965
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.34
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1399.91
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.60
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.62
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.61
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.59
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.74
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.16
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907936
   j =  2                              :            46029
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908214
   j =  2                              :            45884
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 80                 :    0.01
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 90                 :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 93                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 106                :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 107                :  1.9e-3
 
 Anderson-Darling statistic = A2       :    4.85
 p-value of test no 108                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.24
 p-value of test no 115                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.67
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.49
 p-value of test no 120                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.60
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.51
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.28
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.87
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.67
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.15
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.59
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.01
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
 p-value of test no 138                :    0.9938
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  162.58
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.12
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.56
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.37
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.03
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.11
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.52
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.11
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.96
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.07
 p-value of test no 153                :    0.9995    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.66
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.73
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.89
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.97
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.79
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.82
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.48
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.34
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.94
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.38
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.17
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.53
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.08
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.94
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4934.68
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.39
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.50
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.64
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.50
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5071.41
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  431.92
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.33
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.69
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.39
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.79
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.06
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.42
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.78
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.25
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.83
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.26
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.60
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.86
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.18
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12065.35
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12025.08
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.54
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999815798
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.23
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999874928
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 238                :    0.31
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 253                :    0.33
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:47.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  75  RandomWalk1 J (L=50, r=25)      0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35671
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5462
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7173
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 33                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     328
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.73
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.38
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.24
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.98
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.39
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.62
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.46
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.54
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.77
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1417.55
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7069.65
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.67
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.91
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   93.57
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4855.62
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46094
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870094
   j =  1                              :        399907814
   j =  2                              :            46090
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908674
   j =  2                              :            45660
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    4.95
 p-value of test no 85                 :  3.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-5
 p-value of test no 113                :    0.99
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.85
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.61
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.05
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.22
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.34
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.21
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.59
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.44
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.35
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.76
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.01
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.29
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.74
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.11
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.93
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.73
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.83
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.95
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.39
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.67
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.09
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.51
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.42
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.63
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.72
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.91
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.29
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.59
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.83
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.19
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.55
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.41
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.68
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.33
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.35
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.33
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.20
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.72
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 177                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.19
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.00
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.42
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.86
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 210                :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.29
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10234.31
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.56
 p-value of test no 217                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4801.78
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 225                :    0.9978
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.23
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.00
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.79
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12135.46
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11869.71
 p-value of test no 230                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.14
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999991316
 
 Normal statistic for number of bits   :  -0.069
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.11
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999972026
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.31
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.83
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:14.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35672
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4453
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.39
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.11
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    3.32
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 30                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 40                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.71
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.77
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.12
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.83
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.76
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.98
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.67
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.71
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.76
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.02
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.96
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.32
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.32
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 64                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.52
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.76
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4938.26
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908523
   j =  2                              :            45731
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908411
   j =  2                              :            45787
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 74                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 88                 :    0.9948
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
 p-value of test no 113                :  6.3e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.027
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.062
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 118                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.42
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.36
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.09
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.94
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.73
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.20
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.22
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.35
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.93
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.81
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.54
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17035.97
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.97
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.55
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.84
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.35
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.68
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.42
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.35
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.64
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.79
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.73
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.60
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.61
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.30
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.27
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.16
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.22
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.06
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.88
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.35
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.55
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.63
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.33
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.29
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.07
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.41
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.10
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.50
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.26
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.34
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.19
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 183                :    0.31
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.75
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.70
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.19
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.68
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.68
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.08
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.24
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.08
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4193.70
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.21
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11969.43
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.90
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999968561
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.53
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999846185
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.012
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.14
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.62
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:43.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35673
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5361
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     938
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 38                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    2.31
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.05
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 47                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.84
 p-value of test no 48                 :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.57
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.60
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.66
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.64
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.04
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.55
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.72
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1484.49
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.07
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.26
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.08
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.84
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.85
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908155
   j =  2                              :            45918
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45949
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869949
   j =  1                              :        399908108
   j =  2                              :            45937
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 73                 :    0.9997    *****
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 74                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9989
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 109                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 117                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.42
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.20
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.74
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.17
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.63
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.42
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
 p-value of test no 127                :    0.9944
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.58
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.46
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.85
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.09
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.50
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.67
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.02
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.94
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.36
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.31
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.17
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.58
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.41
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.52
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.74
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.19
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.41
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.90
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.15
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.26
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.88
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  425.30
 p-value of test no 163                :    0.9932
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.75
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  106.69
 p-value of test no 165                :  7.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.47
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.30
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.56
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.39
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.27
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.31
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.38
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.89
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.92
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.88
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.98
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.04
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.51
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 193                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.88
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.86
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.06
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.67
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.73
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.22
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.53
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.17
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.07
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.12
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.07
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.68
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000098755
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.17
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000006823
 
 Normal statistic for number of bits   :   0.054
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 238                :  6.1e-3
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 243                :    0.24
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  4.6e-3
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 253                :  6.1e-3
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:36.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35674
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 20                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.54
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    4.02
 p-value of test no 32                 :  8.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.65
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.00
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.53
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.89
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.99
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.13
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.77
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.20
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7171.90
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.57
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.81
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.52
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4973.08
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908333
   j =  2                              :            45826
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908198
   j =  2                              :            45895
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.046
 p-value of test no 115                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.52
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.75
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.52
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.68
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.69
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.90
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.44
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 132                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.03
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.049
 p-value of test no 134                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.11
 p-value of test no 135                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.54
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.41
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17298.07
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.29
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.70
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.47
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.33
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.96
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.80
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.67
 p-value of test no 152                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.68
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.52
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.11
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.88
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.32
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.05
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.85
 p-value of test no 159                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.67
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.47
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.48
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.86
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.92
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.60
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.56
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.31
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5125.56
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.46
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.21
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.61
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.27
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.69
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  312.98
 p-value of test no 174                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.51
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.42
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 179                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    0.89
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.96
 p-value of test no 196                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.15
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.94
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.01
 p-value of test no 207                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.52
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.14
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.11
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.092
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.17
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.86
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.99
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.13
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.90
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.45
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.67
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000014194
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 232                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999918650
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:54.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35675
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 22                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     112
 p-value of test no 43                 :    0.9993    *****
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.22
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.72
 p-value of test no 47                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.42
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.75
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.17
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.90
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.32
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.74
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.81
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1346.07
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.69
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.60
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 63                 :    0.9910
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.39
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.13
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.72
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.00
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45937
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869937
   j =  1                              :        399908130
   j =  2                              :            45929
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 6.93e-5
 p-value of test no 110                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.20e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.80
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.13
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.19
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.76
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.09
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.29
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.89
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.54
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.97
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17341.60
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.86
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.52
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.22
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   50.01
 p-value of test no 149                :  1.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.77
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.23
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.25
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.52
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.43
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.06
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.24
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.92
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.47
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.66
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.93
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.03
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.09
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.94
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.96
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.56
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.91
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.30
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.19
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.88
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.27
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.02
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.03
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.21
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.82
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.90
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.82
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.05
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.96
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.87
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.33
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.36
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4748.17
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.34
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.42
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11644.72
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.85
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.89
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000076984
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 232                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.15
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000029257
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 235                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 252                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 253                :    0.04
 
 Sample variance                       :    3.08
 p-value of test no 254                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:29.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs NJumps, t = 16       0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35676
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 6                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7458
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.94
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     653
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    7.02
 p-value of test no 44                 :  3.4e-4    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.15
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.21
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.97
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.80
 p-value of test no 49                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.21
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.02
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.33
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.23
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.89
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.04
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.15
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.94
 p-value of test no 61                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.42
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.50
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.87
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45958
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869958
   j =  1                              :        399908088
   j =  2                              :            45950
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908477
   j =  2                              :            45760
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 85                 :    0.9973
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 103                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.08
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.30
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.18
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.49
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.99
 p-value of test no 123                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.66
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.58
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.24
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.72
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.48
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.90
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17498.62
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.39
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.54
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.53
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.92
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.22
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.16
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.46
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.14
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.82
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.60
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.88
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.36
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.31
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.34
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.25
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.01
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.24
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.14
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.09
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5172.23
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.56
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.38
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.04
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.88
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.88
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.09
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.07
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.46
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.91
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.57
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.70
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.11
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.24
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.26
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.06
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.42
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.71
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.66
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.93
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11785.35
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11652.01
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.73
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000055495
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.05
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999986000
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:34:59.90
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  25  ClosePairs mNP2, t = 16         3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35677
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5531
 p-value of test no 13                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.16
 p-value of test no 22                 :    0.9974
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    3.87
 p-value of test no 24                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     963
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.30
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.40
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.18
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.21
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.72
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.56
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.50
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.32
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  183.24
 p-value of test no 54                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.35
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1507.78
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6864.90
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.57
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.74
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.59
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.86
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908444
   j =  2                              :            45775
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907933
   j =  2                              :            46032
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 87                 :    0.9959
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 113                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.78
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.12
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.74
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.64
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.52
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.75
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.66
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.04
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.19
 p-value of test no 135                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.00
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17344.44
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.07
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.62
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.10
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.16
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.21
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.39
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.28
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.60
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.52
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.73
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.78
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.31
 p-value of test no 160                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.31
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.83
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.48
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.84
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  121.32
 p-value of test no 165                :  4.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.46
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.84
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.59
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.33
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.19
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.45
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.68
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.50
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.53
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.44
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.53
 p-value of test no 176                :    0.9905
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 183                :    0.98
 
 Sample variance                       :    2.40
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 188                :    0.71
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.34
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.09
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.12
 p-value of test no 203                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.23
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.34
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.76
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 216                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4877.71
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5085.44
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.35
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.88
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11893.02
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11860.47
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.60
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000029197
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.03
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000022969
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.50
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.51
 p-value of test no 249                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:38.81
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35678
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 9                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 17                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.72
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.69
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.19
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.16
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.17
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.20
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.05
 p-value of test no 53                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.87
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  500.36
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.43
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6909.25
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 60                 :    0.9951
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.95
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.71
 p-value of test no 65                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.23
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.47
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5169.43
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908451
   j =  2                              :            45773
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908440
   j =  2                              :            45771
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-4
 p-value of test no 72                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 73                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 74                 :  9.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  1.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 86                 :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 109                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
 p-value of test no 110                :    0.87
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.76
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.62
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.01
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.20
 p-value of test no 123                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.80
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.34
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.90
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.30
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.17
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.60
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17270.34
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.15
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.94
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.90
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.02
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.60
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.28
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.15
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.84
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.64
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.81
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.18
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.70
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.67
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.80
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.16
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.24
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.69
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.05
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.08
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.64
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.91
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.20
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.20
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.06
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.49
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.87
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.78
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.71
 p-value of test no 175                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.57
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 183                :    0.53
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 185                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 188                :    0.03
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.69
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.08
 p-value of test no 198                :    0.9977
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.17
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.23
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10088.20
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.07
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 216                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4723.52
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.44
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.67
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.66
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.20
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.94
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.82
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999814733
 
 Normal statistic for number of bits   :   -1.46
 p-value of test no 232                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.12
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999915710
 
 Normal statistic for number of bits   :   -0.67
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 238                :    0.98
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    0.56
 p-value of test no 249                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 250                :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 252                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:48.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35679
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 19                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7462
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9946
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 29                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.99
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.75
 p-value of test no 46                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.17
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.39
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.09
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.53
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.36
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.94
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.21
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.89
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.53
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 60                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.54
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.27
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.67
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.30
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5164.30
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908010
   j =  2                              :            45989
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908055
   j =  2                              :            45962
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 107                :    0.01
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 115                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.27
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.89
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.78
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.27
 p-value of test no 121                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.59
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.20
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.93
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.25
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.41
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.87
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.92
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.73
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.42
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.08
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.98
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.04
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.42
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.25
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.77
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.72
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.79
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.07
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  107.62
 p-value of test no 157                :    0.9927
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.52
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.13
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.29
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.49
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.61
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.12
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.95
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.12
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.29
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.85
 p-value of test no 168                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.67
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.49
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.39
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.34
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.07
 p-value of test no 173                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.83
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.54
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.24
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 183                :    0.86
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 188                :    0.39
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.23
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.81
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.80
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.88
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.58
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.00
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 218                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.90
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4921.83
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4069.50
 p-value of test no 227                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.30
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11642.72
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12180.57
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.92
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000116962
 
 Normal statistic for number of bits   :    0.92
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.80
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000028501
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 246                :    0.01
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:44.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35680
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 4                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    2.07
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.24
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.45
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.20
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.88
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.91
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.07
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.96
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.96
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.12
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.64
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.77
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7107.58
 p-value of test no 57                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.16
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.00
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.32
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.85
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4969.70
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 70                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908241
   j =  2                              :            45872
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46134
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870134
   j =  1                              :        399907734
   j =  2                              :            46130
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
 p-value of test no 91                 :    0.9980
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 105                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 108                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 118                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.73
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.09
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.75
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.76
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.36
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.93
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.63
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.44
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.15
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.41
 p-value of test no 135                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.79
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16970.62
 p-value of test no 145                :    0.9934
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.41
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.41
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.51
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.67
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.19
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.57
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.96
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.77
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.59
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.54
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.66
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.78
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.21
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.84
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.96
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.57
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.90
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.02
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.26
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.12
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.06
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4922.51
 p-value of test no 168                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.48
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.75
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.20
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.82
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.59
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.56
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.95
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.90
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.38
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.26
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 180                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 188                :    0.18
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.51
 p-value of test no 196                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.36
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.49
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.72
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 209                :    0.92
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.22
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.25
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4716.95
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.52
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4309.71
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.29
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11837.31
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.11
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.06
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000102478
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.44
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999894668
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 243                :    0.08
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.87
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:18.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35681
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 3                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5366
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    6982
 p-value of test no 19                 : 1 -  3.8e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7126
 p-value of test no 20                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.32
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     959
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.66
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.05
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.73
 p-value of test no 48                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.09
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.25
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.21
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.85
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.36
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.81
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.34
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.90
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.36
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.30
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.04
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.69
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.41
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908441
   j =  2                              :            45772
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907687
   j =  2                              :            46152
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 102                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 110                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
 p-value of test no 112                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.92
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.35
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.27
 p-value of test no 121                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.26
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.54
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.51
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.24
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.30
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.45
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.94
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17369.67
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.29
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.63
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.26
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.16
 p-value of test no 149                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.47
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.97
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.32
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.25
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.18
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.22
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  172.09
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.81
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.82
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.02
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.47
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.26
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.45
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.02
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.55
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.31
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.00
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.22
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.00
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.53
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.87
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.96
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.99
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.22
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.74
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.72
 p-value of test no 198                :  7.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.78
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.17
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9824.71
 p-value of test no 211                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9817.52
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.37
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.36
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.19
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.56
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11448.56
 p-value of test no 229                :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12050.41
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.40
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999880496
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.79
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  8000017386
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:33.60
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  19  BirthdaySpacings, t = 8        1 -  3.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35682
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 7                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 12                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.25
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.11
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.88
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.73
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.98
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.68
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.10
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.30
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.74
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.14
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 60                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.69
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.29
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.75
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.63
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.62
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908405
   j =  2                              :            45790
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908308
   j =  2                              :            45840
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9947
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.90
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.37
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.43
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.21
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.31
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.05
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.54
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.53
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.05
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.77
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.70
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   95.32
 p-value of test no 141                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.82
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.42
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.17
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.26
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.10
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.42
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.54
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.58
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.99
 p-value of test no 154                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.24
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.70
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.26
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.59
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.23
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.40
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.26
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.00
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.38
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.79
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.39
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.61
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.98
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.78
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.94
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.67
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.02
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.92
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.06
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.96
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.12
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.95
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.22
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.99
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.78
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.15
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.18
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.23
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.84
 p-value of test no 222                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.44
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.75
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4003.88
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4358.31
 p-value of test no 228                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.92
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.45
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.30
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000020416
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.42
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000126913
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 243                :    0.83
 
 Sample variance                       :    1.95
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    2.18
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:03.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35683
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 12                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 22                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    3.05
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    3.82
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     663
 p-value of test no 31                 :  5.9e-3
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    2.10
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.55
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 42                 :    0.9933
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.72
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.01
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.84
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.50
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.06
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.77
 p-value of test no 51                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.70
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.11
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.03
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.30
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.27
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.13
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.70
 p-value of test no 66                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.75
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.72
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908564
   j =  2                              :            45712
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908051
   j =  2                              :            45970
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.26
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.05
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.59
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.21
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.79
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.80
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.57
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.64
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.92
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17588.97
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.41
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.45
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.34
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.78
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.01
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.75
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.71
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.50
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.00
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.77
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.54
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.30
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.41
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.53
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.09
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.15
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.94
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.71
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.93
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.06
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.40
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.34
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.80
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 172                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.86
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.03
 p-value of test no 174                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.20
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.34
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.12
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.69
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.14
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 205                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    4.30
 p-value of test no 206                :  6.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  249.36
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.49
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.69
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.68
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.77
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.47
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3943.06
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.47
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11797.60
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.37
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999977954
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.78
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999888812
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.49
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 246                :    0.97
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 247                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.88e-4
 p-value of test no 250                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 253                :  6.1e-3
 
 Sample variance                       :    1.84
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:15.77
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35684
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1251
 p-value of test no 4                  :    0.9990    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334371
   j =  1                              :        599997498
   j =  2                              :             1251
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 12                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5320
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4478
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    5.01
 p-value of test no 24                 :  2.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    2.42
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    2.51
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.99
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.40
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.41
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.51
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.08
 p-value of test no 52                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.63
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  191.73
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.08
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.26
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.37
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 58                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.16
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.85
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.17
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.31
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4970.77
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907650
   j =  2                              :            46169
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45670
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869670
   j =  1                              :        399908664
   j =  2                              :            45662
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 78                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.54
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.36
 p-value of test no 115                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.28
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.87
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.01
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.37
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.23
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.17
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.22
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.48
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.48
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.00
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  163.00
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.90
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.71
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.63
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.53
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.52
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.79
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.32
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.64
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.11
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.91
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.75
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.84
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.77
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.64
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.83
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.20
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.98
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.87
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.81
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.85
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  310.55
 p-value of test no 167                :    0.9976
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5241.61
 p-value of test no 168                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.22
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.44
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.82
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.33
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.08
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.15
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.03
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.31
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.96
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 183                :    0.71
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    1.63
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 195                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.10
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.26
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.14
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9857.29
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.052
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.46
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.04
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3964.42
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4001.56
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.99
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.24
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.35
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000042970
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.16
 p-value of test no 233                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000013498
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   4  CollisionOver, t = 2            0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35685
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1275
 p-value of test no 12                 :    0.9923
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334395
   j =  1                              :        599997450
   j =  2                              :             1275
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5464
 p-value of test no 13                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4212
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9916
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9980
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.20
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.79
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.50
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.22
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.03
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.79
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.20
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.10
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.47
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.94
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.66
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.30
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.09
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.33
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.19
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.39
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.30
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5147.65
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908384
   j =  2                              :            45805
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
 p-value of test no 98                 :    0.9975
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.75e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.79e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.95e-4
 p-value of test no 113                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.21
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.20
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.02
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.92
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.18
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.01
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.56
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.98
 p-value of test no 134                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 137                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.55
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17249.78
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.30
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.28
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.07
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.56
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.42
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.28
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.21
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.27
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.99
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.15
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.41
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.86
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.38
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.58
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  196.74
 p-value of test no 161                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.50
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.47
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.28
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.57
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.87
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.17
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.75
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.53
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.90
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.56
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.75
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.69
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.53
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.15
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.39
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.68
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 183                :    0.66
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.38e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.16
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.26
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.10
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.64
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.68
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.057
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4766.00
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.68
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.77
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.23
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.70
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11548.19
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.59
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000004570
 
 Normal statistic for number of bits   :   0.036
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.70
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999946343
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 252                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.60
 p-value of test no 253                :  4.6e-3
 
 Sample variance                       :    2.53
 p-value of test no 254                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:24.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35686
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4285
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 45                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.05
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.20
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.66
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.86
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.56
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.86
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.13
 p-value of test no 55                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.21
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6935.73
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.99
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   39.37
 p-value of test no 65                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.06
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.64
 p-value of test no 67                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.09
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46153
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870153
   j =  1                              :        399907695
   j =  2                              :            46151
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45773
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869773
   j =  1                              :        399908457
   j =  2                              :            45767
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 80                 :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 106                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.23
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.23
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.76
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.27
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.83
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.36
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.65
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 126                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.36
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.50
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.69
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.85
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.26
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17454.60
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.15
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.86
 p-value of test no 148                :    0.9936
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.23
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.75
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.06
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.34
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.06
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.22
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.21
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.89
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.20
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.23
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.61
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.15
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.11
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.44
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.28
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.19
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.00
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.30
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.90
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.35
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.39
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  242.44
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.99
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.83
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.80
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.95
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.95
 p-value of test no 176                :  5.6e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.70
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.20
 p-value of test no 184                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.85
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.97
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 205                :    0.9910
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  161.98
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.18
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.91
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 220                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5077.67
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.52
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.56
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.43
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.00
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11661.07
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.35
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999957161
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.24
 p-value of test no 233                :  7.9e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000007603
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 243                :    0.15
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.024
 p-value of test no 253                :    0.51
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35687
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997179
   j =  2                              :             1409
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5278
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     949
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.47
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    4.03
 p-value of test no 44                 :  8.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.20
 p-value of test no 47                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.46
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.59
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.97
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.36
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.90
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.80
 p-value of test no 53                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.66
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.77
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.60
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7119.56
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.46
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.53
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.67
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.52
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.48
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9946
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908136
   j =  2                              :            45926
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45768
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869768
   j =  1                              :        399908468
   j =  2                              :            45760
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 83                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 85                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
 p-value of test no 91                 :    0.9903
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 92                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    5.51
 p-value of test no 99                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.84
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.16
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   99.72
 p-value of test no 121                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.26
 p-value of test no 123                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.44
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.57
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.19
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.95
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 137                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.50
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17251.02
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.03
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.87
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.25
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.60
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.19
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.05
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.28
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.27
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.60
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.88
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.44
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.29
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.13
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.50
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.98
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.09
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.88
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.04
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.96
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.23
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.17
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.41
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.61
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.27
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.12
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.79
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.70
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.97
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.42
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.80
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.22
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.16
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.88
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.24
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.95
 p-value of test no 198                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.81
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.68
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10116.43
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
 p-value of test no 213                :    0.9936
 
 Anderson-Darling statistic = A2       :    3.68
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9629.11
 p-value of test no 215                :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.19
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.60
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.69
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.18
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.23
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.77
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.34
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000029647
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   97.39
 p-value of test no 233                :  2.7e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999811157
 
 Normal statistic for number of bits   :   -1.49
 p-value of test no 234                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 243                :    0.36
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.19
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.38
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:05.79
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             2.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35688
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5327
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7512
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 28                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.67
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.17
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.76
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.71
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.76
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.74
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.66
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7206.18
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.43
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.82
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.07
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4783.85
 p-value of test no 68                 :    0.9950
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46003
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870003
   j =  1                              :        399907996
   j =  2                              :            45999
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908210
   j =  2                              :            45892
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 78                 :    0.9989
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 111                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.72
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.33
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.75
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.41
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.39
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.19
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.82
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.94
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.04
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17558.39
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.70
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.09
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.77
 p-value of test no 148                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.07
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.83
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.11
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.28
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.00
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.64
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.53
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.47
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.73
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.06
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.26
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.47
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  415.73
 p-value of test no 163                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.97
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.72
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.29
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.01
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5157.16
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.49
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.11
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.61
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.84
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.55
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.58
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.74
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.08
 p-value of test no 176                :    0.9950
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.84
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 183                :    0.84
 
 Sample variance                       :    1.25
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.32
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 200                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    5.55
 p-value of test no 202                :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  144.18
 p-value of test no 203                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.79
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.20
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.75
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.73
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.23
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.61
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.18
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.23
 p-value of test no 229                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.17
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.38
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000007654
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.00
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999926753
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.76
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:04.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35689
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7463
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    1.81
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.93
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.47
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.21
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.16
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.71
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.44
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.65
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.22
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.22
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.95
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.91
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 60                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.37
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.79
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.90
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.55
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  5.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907924
   j =  2                              :            46029
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45594
 p-value of test no 71                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869594
   j =  1                              :        399908817
   j =  2                              :            45584
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 79                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.99
 p-value of test no 119                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.80
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.51
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.55
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.51
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.68
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.36
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.46
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.15
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17274.03
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.73
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.79
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.69
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.43
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.88
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.87
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.78
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.31
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.50
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.06
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.49
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.97
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.61
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.68
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.08
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.04
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.70
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.94
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.32
 p-value of test no 166                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.66
 p-value of test no 167                :    0.9935
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5203.65
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.57
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.07
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.96
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.13
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.85
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.51
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.03
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.00
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.24
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.78
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.96
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :7.02e-17
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.69
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.22
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  7.7e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.27
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.25
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.26
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.16
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.34
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5039.64
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4129.49
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.53
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.92
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11957.25
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999981440
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.28
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999867662
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35690
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4426
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 34                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 46                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.06
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.27
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.08
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.55
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.47
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.32
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.81
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.63
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.68
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.93
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.54
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.11
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.01
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  184.74
 p-value of test no 67                 :  1.1e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4862.66
 p-value of test no 68                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908701
   j =  2                              :            45642
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908052
   j =  2                              :            45971
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 72                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
 p-value of test no 97                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 116                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 9.75e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.04
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.66
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.38
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.74
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.35
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.19
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.71
 p-value of test no 129                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.40
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.33
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.47
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17715.49
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.48
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.55
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.47
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.57
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.01
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.22
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.31
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.69
 p-value of test no 154                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.52
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.23
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.64
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.70
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.61
 p-value of test no 159                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.01
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.42
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.42
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.47
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.71
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.75
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.38
 p-value of test no 166                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.55
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.00
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.40
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.03
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.75
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.45
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.60
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.39
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.36
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.47
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.67
 p-value of test no 178                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.74
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.57
 p-value of test no 189                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.79
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.83
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.93
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.10
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.68
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10249.60
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.17
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.86
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.57
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4339.46
 p-value of test no 228                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11358.39
 p-value of test no 229                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11928.97
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.45
 p-value of test no 231                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  8000001606
 
 Normal statistic for number of bits   :   0.013
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.30
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000056905
 
 Normal statistic for number of bits   :    0.45
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.13
 p-value of test no 237                :    0.9995    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.034
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 243                :    0.06
 
 Sample variance                       :    1.29
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.09
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  41  Permutation, t = 5              1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35691
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 24                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.91
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.44
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.32
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.33
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.40
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.38
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.24
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.77
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1338.62
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.89
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.82
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 64                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.44
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.23
 p-value of test no 66                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.06
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.46
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46141
 p-value of test no 70                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870141
   j =  1                              :        399907721
   j =  2                              :            46135
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45749
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869749
   j =  1                              :        399908507
   j =  2                              :            45739
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 92                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.41
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.15
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.83
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.14
 p-value of test no 122                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.51
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.88
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.21
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 132                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.40
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.03
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.46
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17083.16
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.36
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.38
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.06
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.53
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.37
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.77
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.78
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.50
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.82
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  432.23
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.34
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.84
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.84
 p-value of test no 161                :    0.9907
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.24
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  456.13
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.89
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.67
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.09
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.26
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.90
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.07
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.95
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.82
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.87
 p-value of test no 172                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.09
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.61
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.97
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.17
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.73
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 185                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.75
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.88
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.83
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.37
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9903.07
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.00
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 217                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4855.62
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5032.97
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.52
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3958.36
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.92
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11918.83
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.68
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999906227
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.28
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000044950
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 238                :    0.75
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 252                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:35.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35692
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4157
 p-value of test no 16                 :    0.9969
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.12
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.41
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   23.77
 p-value of test no 47                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.66
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.90
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.66
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.40
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.35
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.41
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.94
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.88
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.56
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.28
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.20
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.89
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.70
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.93
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908006
   j =  2                              :            45994
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907937
   j =  2                              :            46024
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
 p-value of test no 97                 :    0.9947
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 105                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.85e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.90
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.96
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.73
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.89
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.92
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.73
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.33
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.17
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 142                :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17138.18
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.83
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.90
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.69
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.90
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.30
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.68
 p-value of test no 151                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.73
 p-value of test no 152                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.37
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.42
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.78
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.27
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.97
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.98
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.88
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.91
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.66
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.53
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.91
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.37
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.29
 p-value of test no 167                :    0.9973
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.19
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.38
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.27
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.12
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.68
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.86
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.40
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.22
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.90
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.63
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 187                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 201                :    0.9975
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.52
 p-value of test no 203                :    0.9938
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.72
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10057.85
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.35
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.27
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.40
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.77
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.16
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11732.48
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.58
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.46
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999863987
 
 Normal statistic for number of bits   :   -1.08
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.24
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999950057
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.050
 p-value of test no 238                :    0.52
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:26.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35693
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 11                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 24                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.32
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.55
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.36
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.83
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.79
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.27
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.69
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.63
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.57
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.75
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.14
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.44
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46243
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870243
   j =  1                              :        399907516
   j =  2                              :            46239
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45797
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869797
   j =  1                              :        399908406
   j =  2                              :            45797
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 95                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 100                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 4.28e-4
 p-value of test no 110                :  6.5e-4    *****
 
 Anderson-Darling statistic = A2       :    7.37
 p-value of test no 111                :  2.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.00e-6
 p-value of test no 112                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.72
 p-value of test no 119                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.13
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.24
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.40
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.45
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.36
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.43
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 126                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 128                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.61
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.23
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 135                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.51
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17331.86
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.41
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.97
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.52
 p-value of test no 148                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.63
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.40
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.73
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.52
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.35
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.27
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.00
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.88
 p-value of test no 156                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.04
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.22
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.35
 p-value of test no 159                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.18
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.89
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.32
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.15
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.34
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.42
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.30
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.61
 p-value of test no 167                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4914.41
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.90
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.37
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.63
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.11
 p-value of test no 172                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.32
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.88
 p-value of test no 174                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.12
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.75
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.24
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 183                :    0.14
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 190                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.77
 p-value of test no 198                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.75
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.52
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.72
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9961.09
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5014.68
 p-value of test no 222                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5031.14
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.45
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4187.54
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.11
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.42
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.62
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999996023
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000053710
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 238                :    0.66
 
 Sample variance                       :    1.27
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    1.74
 p-value of test no 244                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:17.54
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0               2.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35694
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 10                 :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    5.70
 p-value of test no 24                 :  1.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     991
 p-value of test no 25                 :  1.5e-3
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    4.26
 p-value of test no 27                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 30                 :    0.9925
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     582
 p-value of test no 31                 :    0.76
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.54
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.98
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.27
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.47
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.13
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.61
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.35
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.12
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.18
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.33
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.84
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4885.03
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46242
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870242
   j =  1                              :        399907517
   j =  2                              :            46240
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908044
   j =  2                              :            45975
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 84                 :    0.9932
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.91
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.41
 p-value of test no 120                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.83
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.85
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.34
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.93
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.54
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.52
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.51
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.52
 p-value of test no 134                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.52
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17302.52
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.07
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.56
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.71
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.99
 p-value of test no 150                :  8.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.07
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.25
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.10
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.60
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.62
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.84
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.22
 p-value of test no 157                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.39
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.89
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.95
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.86
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.36
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.92
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.69
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.30
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.60
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.95
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.37
 p-value of test no 168                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.08
 p-value of test no 169                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.93
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.06
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.08
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4915.89
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.55
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.63
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.74
 p-value of test no 176                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.52
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 188                :    0.95
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 192                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.47
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.97
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.17
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.09
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.47
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.24
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.54
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 218                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.92
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4663.59
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3989.32
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.04
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.13
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.74
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.86
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999974456
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.48
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999939566
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.010
 p-value of test no 248                :    0.50
 
 Sample variance                       :    1.03
 p-value of test no 249                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:47.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35695
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 11                 :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 45                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.47
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.45
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.48
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.50
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.78
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.24
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.27
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.61
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.06
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.99
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.79
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.94
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.22
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.79
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.26
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.09
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.67
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908886
   j =  2                              :            45548
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908590
   j =  2                              :            45699
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 78                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.09
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.86
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.01
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.71
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.09
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.73
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 126                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.23
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.21
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.18
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.60
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17628.03
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.05
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.62
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.32
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.04
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.46
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.75
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.19
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.27
 p-value of test no 154                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.98
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.49
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.88
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.14
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.29
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.72
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.79
 p-value of test no 161                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.55
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.54
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.26
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.27
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.25
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.24
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4938.99
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.55
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.11
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.86
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.73
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.75
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.97
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.86
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.34
 p-value of test no 176                :    0.9926
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 183                :    0.07
 
 Sample variance                       :    2.02
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.15
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.10
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.28
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 200                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.32
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.09
 p-value of test no 207                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.05
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9957.74
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.09
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5071.36
 p-value of test no 226                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.61
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.39
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.37
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11868.33
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.57
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000064486
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999982214
 
 Normal statistic for number of bits   :   -0.14
 p-value of test no 234                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 236                :    0.89
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 243                :    0.33
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.58
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.32
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35696
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4429
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4169
 p-value of test no 17                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 19                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.9904
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    2.01
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.31
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.34
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.35
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.37
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.43
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.51
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.03
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.79
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.75
 p-value of test no 56                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6892.91
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.67
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.53
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.39
 p-value of test no 66                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.97
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.23
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46084
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870084
   j =  1                              :        399907834
   j =  2                              :            46080
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46148
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870148
   j =  1                              :        399907708
   j =  2                              :            46140
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 73                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 95                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 2.34e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.61e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
 p-value of test no 113                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.09
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.67
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.80
 p-value of test no 120                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.92
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.72
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.96
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.99
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.38
 p-value of test no 129                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.47
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.47
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.23
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17626.14
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.15
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.47
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.03
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.03
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.68
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.67
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.58
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.62
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.97
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.20
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.80
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.03
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.75
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.91
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.39
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.25
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.97
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.84
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.50
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.77
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.25
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.04
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4809.94
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.93
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.56
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.11
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.14
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.15
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.54
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.01
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.81
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.73
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.24
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.72
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-4
 p-value of test no 204                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  248.43
 p-value of test no 207                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.99
 p-value of test no 211                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.00
 p-value of test no 215                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 218                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.53
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.36
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.76
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.76
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.78
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11890.11
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.13
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999975512
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000039715
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.97
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.99
 p-value of test no 244                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 248                :    0.78
 
 Sample variance                       :    0.41
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.78
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:04.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35697
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 4                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 10                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5262
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7089
 p-value of test no 15                 :    0.9964
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    2.40
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     633
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.12
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.31
 p-value of test no 47                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.59
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.68
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.42
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.65
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.23
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.90
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.57
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.83
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.93
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6969.50
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.17
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.19
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.55
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.85
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5081.18
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45727
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869727
   j =  1                              :        399908550
   j =  2                              :            45719
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908632
   j =  2                              :            45678
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 97                 :  6.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    4.25
 p-value of test no 99                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.63
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.064
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 118                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.65
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.99
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.57
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.96
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.63
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.26
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.94
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.99
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.25
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.42
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.26
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-3
 p-value of test no 142                :    0.9983
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17822.73
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.08
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.00
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.32
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.88
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.91
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.85
 p-value of test no 151                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.92
 p-value of test no 152                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.75
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.37
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.70
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 156                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.14
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.30
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.42
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.58
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.76
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.40
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.58
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.93
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.25
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.86
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5198.34
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.30
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.73
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.49
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.62
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.78
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.77
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  239.70
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.37
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.14
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.68
 p-value of test no 179                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.39
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.93
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.29
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.73
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-4
 p-value of test no 208                :    0.9994    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.40
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10203.00
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9900.68
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 218                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.98
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.56
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.23
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.20
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.33
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11979.41
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.85
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999820799
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.52
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999984695
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.16
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.38
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.48
 p-value of test no 254                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:54.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35698
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 11                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 12                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 23                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 32                 :    0.9977
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.52
 p-value of test no 34                 :  6.1e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9924
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.88
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.42
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.56
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.13
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.36
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.23
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.23
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.04
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.01
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.46
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7132.08
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.40
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.94
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.39
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.19
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.91
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908629
   j =  2                              :            45681
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45709
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869709
   j =  1                              :        399908587
   j =  2                              :            45699
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 99                 :  4.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 105                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 111                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.67
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.63
 p-value of test no 120                :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.41
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.95
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.53
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 124                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.21
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.47
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.72
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.47
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.25
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.84
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.64
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.25
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.49
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.06
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.18
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.17
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.31
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.37
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.48
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.92
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.04
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.57
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.24
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.78
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.42
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.35
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.20
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.28
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.80
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.41
 p-value of test no 164                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.96
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.99
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.66
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.86
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.62
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.35
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.78
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.89
 p-value of test no 172                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.24
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.55
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.09
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.64
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.27
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.40
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.22
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 183                :    0.18
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.72
 p-value of test no 198                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.48
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.44
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.23
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.55
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 219                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.28
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.47
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4022.63
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4183.82
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.19
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.66
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.83
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000041398
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.69
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000014413
 
 Normal statistic for number of bits   :    0.11
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 238                :    0.36
 
 Sample variance                       :    1.21
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:51.89
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35699
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4589
 p-value of test no 14                 :  7.6e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 15                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4211
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.07
 p-value of test no 23                 :  8.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    3.10
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.75
 p-value of test no 34                 :  1.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.65
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.33
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.45
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.44
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.36
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.80
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.83
 p-value of test no 54                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.48
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.20
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7057.56
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.86
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.19
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.20
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.40
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4953.34
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45838
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869838
   j =  1                              :        399908326
   j =  2                              :            45834
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 71                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907784
   j =  2                              :            46102
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 91                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 104                :    0.9930
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 110                :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-5
 p-value of test no 112                :    0.9940
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 115                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 116                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.57
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.08
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.20
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.78
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.92
 p-value of test no 124                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.53
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.72
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.69
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 143                :    0.9904
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16968.98
 p-value of test no 145                :    0.9936
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.22
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.52
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.34
 p-value of test no 148                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   46.27
 p-value of test no 149                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.70
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.15
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.16
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.75
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.29
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  103.44
 p-value of test no 156                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.38
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.15
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.12
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.31
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.88
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.04
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.87
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.98
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.20
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.03
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.83
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.67
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.90
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.99
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.29
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.49
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5129.51
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.94
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.96
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.08
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.29
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.42
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.96
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.88
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.60
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.64
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.73
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9794.46
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.10
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.37
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.31
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.89
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12013.34
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12074.34
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.81
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000007762
 
 Normal statistic for number of bits   :   0.061
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.63
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999964373
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 238                :    0.74
 
 Sample variance                       :    2.14
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:37.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         7.6e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35700
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1482
 p-value of test no 11                 :  8.6e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334602
   j =  1                              :        599997036
   j =  2                              :             1482
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 12                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.70
 p-value of test no 29                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 40                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.27
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.04
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.29
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.42
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.79
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.61
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.25
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.96
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.73
 p-value of test no 58                 :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 59                 :    0.99
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 60                 :  6.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.51
 p-value of test no 61                 :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.50
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.84
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5030.51
 p-value of test no 68                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45818
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869818
   j =  1                              :        399908365
   j =  2                              :            45816
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45748
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869748
   j =  1                              :        399908506
   j =  2                              :            45744
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 74                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.36
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.27
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.55
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.42
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.10
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.77
 p-value of test no 125                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.02
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.25
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.04
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.05
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17458.17
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.31
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.59
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.29
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.03
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.79
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.05
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.83
 p-value of test no 154                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.01
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.69
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.23
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  585.46
 p-value of test no 158                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.56
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.41
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.53
 p-value of test no 162                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.13
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.16
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.96
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.45
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.96
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4925.92
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.56
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.74
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.94
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.57
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4851.44
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.08
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.58
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.06
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.56
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 192                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.31
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.78
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.40
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9858.98
 p-value of test no 211                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10197.14
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.08
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5117.11
 p-value of test no 222                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.58
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.31
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.95
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11598.11
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12185.73
 p-value of test no 230                :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.64
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  7999930353
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.91
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999893873
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 243                :    0.71
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9978
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.066
 p-value of test no 248                :    0.53
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 253                :    0.81
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:09.03
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           8.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35701
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 8                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.06
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.61
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 45                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.01
 p-value of test no 46                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.38
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.97
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.16
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.07
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.50
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.67
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.37
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.23
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.61
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.88
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.68
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.80
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.32
 p-value of test no 65                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.14
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.27
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.96
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45921
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869921
   j =  1                              :        399908160
   j =  2                              :            45917
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45731
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869731
   j =  1                              :        399908542
   j =  2                              :            45723
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.58
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.14
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.65
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.15
 p-value of test no 120                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.06
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.18
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.22
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.96
 p-value of test no 125                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.16
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.18
 p-value of test no 133                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.030
 p-value of test no 134                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.88
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.59
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17393.79
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.45
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.31
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.48
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.94
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   41.19
 p-value of test no 150                :  8.8e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.05
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.08
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.39
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.31
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.95
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.00
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.80
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.70
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.98
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.70
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.22
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.62
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.37
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.54
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.40
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.28
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.34
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.75
 p-value of test no 169                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.02
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.52
 p-value of test no 171                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.92
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.29
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.74
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.10
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.63
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.79
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.76e-4
 p-value of test no 194                :    0.9946
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 195                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.06
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.04
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.93
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.23
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.23
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.03
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.09
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.03
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.74
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4079.47
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.01
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11988.01
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.01
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000134914
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.99
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000021073
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.47
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:19.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 C (L=50, r=0)       8.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35702
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 12                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5283
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7092
 p-value of test no 19                 :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.44
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     944
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 30                 :    0.9904
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.94
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.85
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.92
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.87
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.29
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.30
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.69
 p-value of test no 53                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.72
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  454.37
 p-value of test no 55                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.83
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6872.75
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 58                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   14.75
 p-value of test no 61                 :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.69
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   96.21
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.09
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908339
   j =  2                              :            45814
   j =  3                              :               11
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.92
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.32
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.61
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.29
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.51
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.81
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.38
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.87
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.93
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.62
 p-value of test no 146                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.71
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.31
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.82
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.16
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.86
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.59
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.82
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.76
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.15
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.53
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.72
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.07
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.67
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.58
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.56
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.81
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.19
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.05
 p-value of test no 165                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.56
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.30
 p-value of test no 167                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.38
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  433.35
 p-value of test no 169                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.25
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.93
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.14
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.33
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.97
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.63
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.86
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.50
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 187                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.67
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.17
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.38
 p-value of test no 207                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.70
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.26
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4904.43
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.09
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.82
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.32
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11990.48
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.52
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.91
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999943238
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.46
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000075583
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 237                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.62
 p-value of test no 244                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:39.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35703
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 12                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 21                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.61
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.67
 p-value of test no 35                 :  4.3e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.13
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.16
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.45
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.84
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.50
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.40
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.69
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.63
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.34
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.00
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.56
 p-value of test no 56                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.80
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.22
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.01
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.23
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.60
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.37
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46091
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870091
   j =  1                              :        399907824
   j =  2                              :            46079
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908747
   j =  2                              :            45622
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.58
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.42
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.06
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.51
 p-value of test no 122                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.86
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.70
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.54
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.27
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.42
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.48
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.08
 p-value of test no 135                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.37
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.39
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.30
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.41
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.87
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.72
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.18
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.96
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.53
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.51
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.39
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.80
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.82
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.73
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.98
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.59
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.29
 p-value of test no 161                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.44
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.54
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.32
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.76
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.67
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.82
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.90
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.19
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.17
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.68
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.53
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.57
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.17
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.20
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.14
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 188                :    0.14
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.86
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.78
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.46
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.88
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9924.09
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.58
 p-value of test no 215                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    4.33
 p-value of test no 221                :  6.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5157.47
 p-value of test no 222                :  3.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.20
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.58
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.88
 p-value of test no 228                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.98
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.09
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.25
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000021223
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.05
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000149191
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.021
 p-value of test no 248                :    0.51
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:07.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35704
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4488
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7171
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 27                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.49
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.95
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.27
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 39                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 46                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.62
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.63
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.64
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.18
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.25
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.72
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.21
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.61
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.21
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.03
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.22
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.61
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.37
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.59
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.41
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45955
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869955
   j =  1                              :        399908093
   j =  2                              :            45949
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908360
   j =  2                              :            45814
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 108                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
 p-value of test no 109                :  7.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.40e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : 8.07e-4
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.54
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.80
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.53
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.55
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.03
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.16
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.52
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.40
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.67
 p-value of test no 135                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.58
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.57
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.95
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.50
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.00
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.41
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.25
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.84
 p-value of test no 151                :  3.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.36
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.22
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.16
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.22
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.56
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.58
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.54
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.18
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.50
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.89
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.20
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.78
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.51
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.38
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.44
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.42
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.14
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.42
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.63
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.65
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4800.33
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.00
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.27
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.70
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.17
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.69
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.97
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.18
 p-value of test no 189                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.50
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.60
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9871.34
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9909.98
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4975.07
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.87
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.16
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.17
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.70
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.64
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.49
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000002341
 
 Normal statistic for number of bits   :   0.019
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.66
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999925565
 
 Normal statistic for number of bits   :   -0.59
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.85
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:44.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35705
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4288
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.60
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.38
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.23
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.55
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.12
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.34
 p-value of test no 53                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.90
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.48
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1602.11
 p-value of test no 56                 :  1.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.56
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.33
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.32
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.13
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.37
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.16
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908910
   j =  2                              :            45545
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 77                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 85                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
 p-value of test no 110                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.29e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.074
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.37
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.12
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.19
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.73
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.57
 p-value of test no 123                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.40
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.01
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.10
 p-value of test no 133                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.97
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17418.26
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.99
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.15
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.81
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.45
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.22
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.09
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.59
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.29
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.86
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.08
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.05
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.95
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.22
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.11
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.74
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.26
 p-value of test no 165                :    0.9935
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.26
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.18
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.61
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.36
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.04
 p-value of test no 170                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.08
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.61
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.88
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.99
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.81
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.68
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.80
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.59
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.75
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.29
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.23
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.81
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10119.30
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.80
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5061.95
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4147.71
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.57
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.36
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.53
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.62
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999882227
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.99
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999984062
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    1.10
 p-value of test no 239                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 243                :    0.89
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:07.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35706
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 6                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 18                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.04
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     855
 p-value of test no 25                 :    0.93
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    4.18
 p-value of test no 36                 :  7.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     255
 p-value of test no 37                 :    0.9957
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 44                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.88
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.77
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.39
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.13
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.39
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.59
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.34
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.09
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.04
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  453.08
 p-value of test no 55                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.05
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.27
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.47
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 63                 :  1.3e-3
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 64                 :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   91.11
 p-value of test no 65                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.95
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.66
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45923
 p-value of test no 70                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869923
   j =  1                              :        399908157
   j =  2                              :            45917
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45924
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869924
   j =  1                              :        399908153
   j =  2                              :            45922
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.64
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.51
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.31
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.51
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.15
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.43
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.04
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.79
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.80
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.38
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.92
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.61
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17494.13
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.90
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.79
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   45.01
 p-value of test no 148                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.68
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.83
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.59
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.61
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.83
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.64
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.82
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.37
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.03
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.88
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.33
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.88
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.96
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.82
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.72
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.12
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.67
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.74
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.31
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.91
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.88
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.10
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.61
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.77
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.33
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.73
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.55
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.21
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 188                :    0.08
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.75
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.34
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.98
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.68
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.73
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.33
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.86
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4791.97
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3955.47
 p-value of test no 227                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.25
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11917.01
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11692.68
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.93
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999990128
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.89
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000062404
 
 Normal statistic for number of bits   :    0.49
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 235                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:58.51
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35707
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    4.59
 p-value of test no 24                 :  4.5e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     981
 p-value of test no 25                 :  4.0e-3
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    3.31
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.58
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.66
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.01
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.44
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.48
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.59
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.89
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.40
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  391.83
 p-value of test no 55                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1525.76
 p-value of test no 56                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7221.31
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.44
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.40
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.47
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   85.52
 p-value of test no 67                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.12
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45725
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869725
   j =  1                              :        399908552
   j =  2                              :            45721
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908528
   j =  2                              :            45733
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 115                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.42
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.85
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.84
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.77
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.77
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.48
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.71
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.42
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.90
 p-value of test no 133                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.93
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.36
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.58
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.92
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.27
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.93
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.55
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.73
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.17
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.12
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.76
 p-value of test no 152                :  3.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.81
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.35
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.64
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.21
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.15
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.21
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.66
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.78
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.14
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.93
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.94
 p-value of test no 163                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.68
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.26
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.61
 p-value of test no 167                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.45
 p-value of test no 168                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.89
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.24
 p-value of test no 170                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.34
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.52
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.73
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.15
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.19
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.28
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.14
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.15
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.44
 p-value of test no 207                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.20
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.55
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 217                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.023
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.86
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.11
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.69
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4334.99
 p-value of test no 228                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11746.97
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12061.68
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.19
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999981155
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.34
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000181093
 
 Normal statistic for number of bits   :    1.43
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.68
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:49.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35708
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997211
   j =  2                              :             1393
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9989
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.47
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.85
 p-value of test no 47                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.13
 p-value of test no 48                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.69
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.42
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 51                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.01
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.54
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.98
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.06
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.72
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.39
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.73
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.66
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.89
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5093.90
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45753
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869753
   j =  1                              :        399908497
   j =  2                              :            45747
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46078
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870078
   j =  1                              :        399907845
   j =  2                              :            46076
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :  9.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 100                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 102                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.70
 p-value of test no 116                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.05
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.45
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.92
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.36
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.67
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.39
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.65
 p-value of test no 133                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.20
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 138                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.73
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 143                :    0.9905
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16969.99
 p-value of test no 145                :    0.9935
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.34
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.46
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.34
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.44
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.22
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.94
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.58
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.68
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.88
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.29
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.44
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.41
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.29
 p-value of test no 161                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.89
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.10
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.79
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.73
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.02
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.87
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.11
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.26
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.21
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.80
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.08
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.68
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.85
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.03
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.40
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.51
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.061
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.63
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.79
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.16
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10141.91
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.93
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5045.50
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 223                :  1.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    5.07
 p-value of test no 225                :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4618.19
 p-value of test no 226                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4154.80
 p-value of test no 227                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.91
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.22
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.56
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.45
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000043885
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.09
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999873815
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.22
 p-value of test no 239                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 242                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    0.92
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 248                :    0.96
 
 Sample variance                       :    1.45
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.42
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  50  SampleProd, t = 8               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35709
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 7                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 12                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4446
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.11
 p-value of test no 22                 :  7.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     333
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 39                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    2.00
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.51
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.06
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.00
 p-value of test no 49                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.39
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.92
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.10
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.58
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.29
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.76
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6946.66
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.93
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.24
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.46
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.53
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45915
 p-value of test no 70                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869915
   j =  1                              :        399908175
   j =  2                              :            45905
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907802
   j =  2                              :            46093
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 112                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.73
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.48
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.59
 p-value of test no 122                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.63
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.99
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.44
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.06
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.74
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.35
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.49
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.67
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.95
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.27
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.13
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.62
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.64
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.74
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.12
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.49
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.89
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.73
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.57
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.25
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.04
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.94
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.99
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.04
 p-value of test no 162                :  4.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.35
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.12
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.05
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.75
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.78
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.02
 p-value of test no 168                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.93
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.79
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.61
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.86
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.74
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.66
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.42
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.17
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.025
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 182                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 194                :    0.50
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.42
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.15
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.58
 p-value of test no 203                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.80
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.02
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10031.40
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.30
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.34
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.18
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.96
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.94
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11686.79
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.75
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999945041
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.07
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999995288
 
 Normal statistic for number of bits   :  -0.037
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  5.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 236                :    0.88
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 237                :  8.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.42
 p-value of test no 238                :    0.9923
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 248                :    0.69
 
 Sample variance                       :    0.40
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:14.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35710
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4556
 p-value of test no 14                 :  4.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 18                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.80
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.45
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.85
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.69
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.73
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.96
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.99
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.75
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1333.57
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7003.53
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.50
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.11
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.21
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.91
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.99
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45827
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869827
   j =  1                              :        399908347
   j =  2                              :            45825
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46048
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870048
   j =  1                              :        399907908
   j =  2                              :            46040
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 118                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.41
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.17
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.48
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.95
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.78
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.20
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.54
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.99
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.00
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.09
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.31
 p-value of test no 135                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.01
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.04
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17683.70
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.87
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.89
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.26
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.00
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.71
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.47
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.14
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.47
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.30
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.76
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.16
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.05
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.47
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.07
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.00
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.08
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.90
 p-value of test no 166                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.50
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.38
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.83
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.20
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.47
 p-value of test no 171                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.47
 p-value of test no 172                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.35
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.40
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.44
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.83
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.98
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.28
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.69
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
 p-value of test no 201                :    0.9942
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  158.37
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.14
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10061.64
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10183.47
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.60
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.15
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.82
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.91
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11602.25
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11835.49
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.17
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999996857
 
 Normal statistic for number of bits   :  -0.025
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.74
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000032995
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.17
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 243                :    0.41
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 248                :    0.31
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.63
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  14  BirthdaySpacings, t = 3         4.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35711
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5510
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 19                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 20                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.50
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.26
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.60
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.89
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.06
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.21
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.62
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  492.62
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.73
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6882.39
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.40
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.26
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.72
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.06
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5079.45
 p-value of test no 68                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908333
   j =  2                              :            45826
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908297
   j =  2                              :            45844
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 77                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 106                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.21
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.62
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.78
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.71
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.92
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.28
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.54
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-3
 p-value of test no 126                :    0.9978
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   63.31
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.76
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.06
 p-value of test no 134                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.80
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17401.99
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.63
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.94
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.76
 p-value of test no 148                :    0.9940
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.97
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.45
 p-value of test no 152                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.44
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.35
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.97
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.12
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.73
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.28
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.39
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.27
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.21
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.65
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.01
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  174.80
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.88
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.97
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.12
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5154.31
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.25
 p-value of test no 169                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.95
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.25
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.85
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.67
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.58
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.41
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.94
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.89
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 183                :    0.10
 
 Sample variance                       :    2.38
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.88
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.19
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.67
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.18
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.95
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.96
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 218                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.57
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.43
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.83
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4258.57
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11613.82
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.63
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.01
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999945728
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000207391
 
 Normal statistic for number of bits   :    1.64
 p-value of test no 234                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 238                :    0.18
 
 Sample variance                       :    1.84
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.099
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 248                :    0.35
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 253                :    0.83
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35712
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 4                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4223
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    4.06
 p-value of test no 27                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 28                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 30                 :    0.9990    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.10
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.69
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.97
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.96
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.43
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.78
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.34
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.11
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.69
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.59
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.81
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.22
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.15
 p-value of test no 65                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.22
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.02
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5005.22
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46033
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870033
   j =  1                              :        399907939
   j =  2                              :            46023
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908374
   j =  2                              :            45810
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 83                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 85                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.60
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 108                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.61
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.95
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.45
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.46
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 123                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.27
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.46
 p-value of test no 125                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.77
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.75
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.26
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.87
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.95
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 143                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17718.77
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.32
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.53
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.16
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.74
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.52
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.09
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.91
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.70
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.36
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.99
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.38
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.08
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.31
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.17
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.25
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.96
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  573.02
 p-value of test no 163                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.71
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.01
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.78
 p-value of test no 167                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.79
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.66
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.03
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.78
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.08
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5193.76
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.61
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.69
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.46
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.92
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.92
 p-value of test no 196                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.26
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.37
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 210                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.20
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.80
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.20
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.46
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.59
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.17
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.53
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.12
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.09
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999893027
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.45
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000000259
 
 Normal statistic for number of bits   : 2.05e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 238                :    0.81
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 243                :    0.72
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.035
 p-value of test no 248                :    0.51
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:37.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35713
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5360
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4504
 p-value of test no 17                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 19                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.12
 p-value of test no 40                 :  8.4e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.83
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.42
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.48
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.98
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.26
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.19
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.11
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  224.40
 p-value of test no 54                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.20
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.23
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7267.54
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 58                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  4.8e-3
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.89
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.31
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.41
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.40
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.81
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907945
   j =  2                              :            46020
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907922
   j =  2                              :            46033
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 84                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.80
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.53
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.72
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.52
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.12
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.71
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.43
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.41
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  6.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    3.60
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   93.29
 p-value of test no 141                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17291.38
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.07
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.58
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.57
 p-value of test no 148                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.68
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.74
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.16
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   15.14
 p-value of test no 152                :    0.9986
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.57
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.06
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.95
 p-value of test no 155                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.58
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.30
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.45
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.60
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.47
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.95
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.62
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.09
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.58
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5023.18
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.83
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.34
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.23
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.74
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.11
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.50
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.48
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.05
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.53
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.38
 p-value of test no 179                :  8.7e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 4.49e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.47
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.04
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.40
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 205                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.78
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.28
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.06
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.39
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.03
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.11
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.12
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.81
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12183.39
 p-value of test no 230                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.34
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000111877
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.12
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999941045
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 238                :    0.42
 
 Sample variance                       :    2.04
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:30.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35714
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5617
 p-value of test no 13                 :  4.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.49
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.21
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.12
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.47
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.43
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.75
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.72
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.38
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.68
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  275.59
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.72
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.75
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6965.13
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.14
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.92
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.67
 p-value of test no 66                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.10
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.16
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46040
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870040
   j =  1                              :        399907925
   j =  2                              :            46030
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45853
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869853
   j =  1                              :        399908297
   j =  2                              :            45847
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 80                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
 p-value of test no 109                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.045
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.78
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.48
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.83
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.55
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.65
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.60
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.90
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.63
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 132                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.12
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.09
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.17
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.42
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.17
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.79
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.87
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.63
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.51
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.35
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.62
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.98
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.65
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.46
 p-value of test no 156                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.30
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.64
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.12
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.19
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.13
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.81
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.79
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.52
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.49
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.03
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.48
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.18
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.34
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.01
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.41
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.20
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4894.36
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.44
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  140.60
 p-value of test no 175                :    0.9995    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.84
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.43
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.24
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 187                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.80
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.08
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.09
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.11
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 208                :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    4.48
 p-value of test no 210                :  5.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9669.85
 p-value of test no 211                :    0.9908
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.44
 p-value of test no 215                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.34
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.01
 p-value of test no 226                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.62
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.05
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.11
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.12
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.30
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999858800
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.55
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000009454
 
 Normal statistic for number of bits   :   0.075
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 236                :  3.9e-3
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 251                :    0.77
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    2.59
 p-value of test no 254                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:42.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 C (L=10000, r=15)   0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35715
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 7                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997195
   j =  2                              :             1401
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 11                 :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 17                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.56
 p-value of test no 23                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    2.01
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.22
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.61
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.65
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.13
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.95
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  282.36
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.59
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.78
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6957.71
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.51
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.88
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.82
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.91
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.44
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9912
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45926
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869926
   j =  1                              :        399908150
   j =  2                              :            45922
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908117
   j =  2                              :            45934
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 73                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9966
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 111                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.49
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.20
 p-value of test no 120                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.89
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.40
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.15
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.39
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 131                :  6.6e-3
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.42
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.27
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17692.97
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.65
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.08
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.98
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.57
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.89
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.52
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.60
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.32
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.11
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.71
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.64
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.43
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.57
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.75
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  104.28
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.81
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.32
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.33
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.66
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.15
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.44
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.67
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.38
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.54
 p-value of test no 169                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.11
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.10
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.75
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.60
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.30
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.13
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.79
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 177                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.59
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 187                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 188                :    0.67
 
 Sample variance                       :    1.54
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.56
 p-value of test no 196                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.36
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.28
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.60
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.84
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.60
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.030
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.52
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.26
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4297.79
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.10
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.59
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.84
 p-value of test no 230                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.55
 p-value of test no 231                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999857456
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.77
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000159547
 
 Normal statistic for number of bits   :    1.26
 p-value of test no 234                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.18
 p-value of test no 239                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 253                :    0.08
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:01.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35716
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 5                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 8                  :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1243
 p-value of test no 12                 :    0.9995    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334363
   j =  1                              :        599997514
   j =  2                              :             1243
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5250
 p-value of test no 13                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 22                 :    0.9928
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.28
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.88
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.98
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.11
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.64
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.84
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.92
 p-value of test no 53                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.62
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.89
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1382.03
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.92
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.42
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.11
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.23
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.97
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.70
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908577
   j =  2                              :            45701
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45848
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869848
   j =  1                              :        399908306
   j =  2                              :            45844
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 73                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 98                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 99                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    3.20
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.19
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.80
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 118                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.32
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.75
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.90
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   77.19
 p-value of test no 123                :  1.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.05
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.28
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.22
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.96
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.81
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.96
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17105.86
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.16
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.37
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.80
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.02
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.19
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.91
 p-value of test no 151                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.50
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.55
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.81
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.43
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.95
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.65
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.56
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.56
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.05
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.08
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.38
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  547.36
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.62
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.76
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.14
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.20
 p-value of test no 167                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.24
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.55
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.14
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.80
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.22
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5117.55
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.64
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.56
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.86
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.16
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 179                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.66
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 188                :    0.09
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.78
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.26
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.66
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 208                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.72
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10167.50
 p-value of test no 215                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 221                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.16
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.79
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.94
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.46
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11993.70
 p-value of test no 229                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12009.88
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.41
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999858809
 
 Normal statistic for number of bits   :   -1.12
 p-value of test no 232                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.75
 p-value of test no 233                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000064624
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.26
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.75
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9977
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.52
 p-value of test no 254                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           0.9995 
  63  WeightDistrib, r = 10           1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35717
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 12                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4452
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    2.16
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 27                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    4.20
 p-value of test no 32                 :  7.0e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.66
 p-value of test no 35                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 41                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.16
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.69
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.52
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.90
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.61
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  485.97
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.48
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6914.55
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.94
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.81
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.92
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.25
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.36
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45634
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869634
   j =  1                              :        399908736
   j =  2                              :            45626
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908562
   j =  2                              :            45713
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 79                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 80                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 90                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
 p-value of test no 107                :    0.9925
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.12
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.58
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.73
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.41
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.68
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.91
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.77
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.46
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.29
 p-value of test no 133                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9909
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.04
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.58
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.76
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.06
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.67
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.17
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.37
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.98
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.74
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.09
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.74
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.25
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.75
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.34
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.62
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.61
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.35
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.19
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.75
 p-value of test no 162                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.24
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.98
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.68
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.25
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.34
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.95
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.95
 p-value of test no 169                :    0.9911
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.63
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.13
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.84
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.16
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.20
 p-value of test no 174                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  153.85
 p-value of test no 175                :    0.9934
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.41
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
 p-value of test no 181                :    0.9974
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.04
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.26
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.25
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.52
 p-value of test no 207                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.41
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.68
 p-value of test no 215                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.84
 p-value of test no 222                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.10
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.69
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.82
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.57
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.26
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.16
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000142936
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.89
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000167032
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.34e-4
 p-value of test no 235                :    0.9993    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.9905
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 248                :    0.13
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 253                :    0.08
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:43.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35718
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 4                  :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 15                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 21                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.04
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 27                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 32                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.76
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    3.07
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.48
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.38
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.40
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.44
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.24
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.80
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.32
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.88
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.42
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.46
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6939.22
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.20
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.50
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.54
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.98
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45714
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869714
   j =  1                              :        399908575
   j =  2                              :            45708
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46241
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870241
   j =  1                              :        399907522
   j =  2                              :            46233
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
 p-value of test no 98                 :    0.9918
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 112                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.12
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.76
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.72
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.39
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.31
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.97
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.35
 p-value of test no 124                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.46
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.21
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.45
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 134                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.94
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 140                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.98
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.31
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.70
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.55
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.70
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.95
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.06
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.75
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.60
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.91
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.25
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.30
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.27
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.73
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.47
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.90
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.87
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.79
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.91
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.25
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.04
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5093.57
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.63
 p-value of test no 169                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.86
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.86
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.71
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5014.51
 p-value of test no 173                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.92
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.68
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.57
 p-value of test no 176                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.54
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.89
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.65
 
 Sample variance                       :    2.29
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-3
 p-value of test no 185                :    0.9989
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 186                :  2.4e-3
 
 Anderson-Darling statistic = A2       :    5.38
 p-value of test no 187                :  2.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.31
 p-value of test no 188                :  4.7e-4    *****
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.75
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.35
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 204                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.26
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.65
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9907
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9999.64
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.69
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.10
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3982.53
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.52
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.54
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.29
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.04
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  8000052405
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.48
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000065587
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.70
 p-value of test no 239                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 247                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:45.35
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35719
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.35
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     640
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.79
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     322
 p-value of test no 37                 :    0.11
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 39                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.35
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.65
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.21
 p-value of test no 47                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.18
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.24
 p-value of test no 49                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.54
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.79
 p-value of test no 51                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.69
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.75
 p-value of test no 53                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.02
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.61
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.83
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7196.51
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.08
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.62
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.27
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5067.96
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907934
   j =  2                              :            46030
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908673
   j =  2                              :            45659
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.91
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.67
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.38
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.02
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.37
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.70
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.62
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.62
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.36
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.26
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17517.37
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.38
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.31
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.05
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.39
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.24
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.17
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.31
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.56
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.46
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.41
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.45
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.45
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.92
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  112.50
 p-value of test no 160                :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.23
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.95
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.44
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.52
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.82
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.22
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.74
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5139.34
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.23
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.76
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.76
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.22
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.56
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.23
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.81
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.80
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.33
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.65
 p-value of test no 196                :    0.79
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.34
 p-value of test no 198                :    0.83
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.56
 p-value of test no 203                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.77
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.92
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9948.11
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 217                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.15
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 224                :    0.96
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.10
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4066.69
 p-value of test no 227                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.97
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12000.45
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.81
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.38
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000286867
 
 Normal statistic for number of bits   :    2.27
 p-value of test no 232                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.98
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999934181
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 238                :    0.08
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.88
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35720
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 6                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 16                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    3.14
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.68
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.75
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.63
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.72
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.71
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.30
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.82
 p-value of test no 51                 :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.35
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.16
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  394.84
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.98
 p-value of test no 56                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.47
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.59
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.14
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.29
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.26
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4918.20
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45574
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908855
   j =  2                              :            45568
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908176
   j =  2                              :            45909
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 87                 :  5.5e-3
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  6.6e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 94                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 102                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.81
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.14
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.28
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.36
 p-value of test no 122                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.97
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.40
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.81
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.97
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.06
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.88
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.65
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.48
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.80
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.44
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.73
 p-value of test no 149                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.49
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.53
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.44
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.36
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.45
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.03
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.62
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.67
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.41
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.11
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.11
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.32
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.41
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.10
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.94
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.90
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.70
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.58
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.96
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.38
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.22
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.71
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.26
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.96
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.97
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.34
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.13
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.34
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 182                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 183                :    0.93
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.17
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.50
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.16
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.77
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.14
 p-value of test no 207                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 210                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.43
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.29
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.15
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.83
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4363.46
 p-value of test no 227                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.23
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11736.10
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12092.60
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.18
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000038989
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.24
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999916145
 
 Normal statistic for number of bits   :   -0.66
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 238                :    0.44
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 248                :    0.23
 
 Sample variance                       :    2.13
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 251                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:29.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35721
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5576
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.22
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.14
 p-value of test no 36                 :    0.9991    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.81
 p-value of test no 47                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.90
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.95
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.55
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.78
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.61
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.45
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.27
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  498.08
 p-value of test no 55                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.12
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7133.27
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.14
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.97
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.25
 p-value of test no 66                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.81
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.52
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45779
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869779
   j =  1                              :        399908443
   j =  2                              :            45777
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45606
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869606
   j =  1                              :        399908794
   j =  2                              :            45594
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 116                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.59
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.24
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.62
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.28
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.87
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.71
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.41
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.32
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.05
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.08
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17457.46
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.96
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.61
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.23
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.07
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.71
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.02
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.23
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.25
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.10
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.83
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.32
 p-value of test no 157                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.09
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.24
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.11
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.07
 p-value of test no 161                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.98
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.07
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   94.29
 p-value of test no 164                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.81
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.02
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.97
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.05
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.22
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.43
 p-value of test no 171                :    0.9979
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.28
 p-value of test no 172                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4871.51
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.15
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.01
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.26
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.61
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 183                :    0.91
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 192                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.21
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.37
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.77
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.49
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4981.10
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 225                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.60
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4078.54
 p-value of test no 227                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.06
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11702.75
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.54
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.39
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999945539
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.85
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999941348
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 253                :    0.64
 
 Sample variance                       :    1.79
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.68
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9          0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35722
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5298
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 21                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 41                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.88
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.02
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.75
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.81
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.39
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.23
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.18
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.07
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1394.26
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7220.19
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 59                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.71
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.98
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.50
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.28
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5192.50
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45870
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869870
   j =  1                              :        399908264
   j =  2                              :            45862
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908297
   j =  2                              :            45844
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
 p-value of test no 113                :    0.23
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.59
 p-value of test no 119                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.30
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.62
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.32
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.00
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.42
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.69
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 127                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.25
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 131                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.92
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.26
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.30
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.05
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.62
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.03
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.70
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.56
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.29
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.79
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.12
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.45
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.63
 p-value of test no 154                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.24
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.06
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.56
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.96
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.49
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.47
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.29
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.09
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.66
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.49
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.71
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.62
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.84
 p-value of test no 168                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.23
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.10
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.81
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.53
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5247.95
 p-value of test no 173                :  7.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.14
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.79
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.38
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.53
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.91
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.69
 p-value of test no 180                :  1.4e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 181                :    0.9925
 
 Anderson-Darling statistic = A2       :    7.94
 p-value of test no 182                :  1.3e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.62
 p-value of test no 183                :    0.9999    *****
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.80
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.44
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.10
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 210                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.85
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10139.40
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 216                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.44
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.58
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.24
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4081.97
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.26
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.89
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.28
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999941417
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.61
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999974801
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 253                :    0.60
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:09.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  82  LempelZiv, r = 0                0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35723
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4206
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 18                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.84
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.44
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.09
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.07
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.46
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.04
 p-value of test no 50                 :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.30
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.21
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.57
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.67
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.00
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.70
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 60                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.93
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.99
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.18
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5159.55
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45718
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869718
   j =  1                              :        399908568
   j =  2                              :            45710
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45433
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869433
   j =  1                              :        399909137
   j =  2                              :            45427
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.23
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 107                :  3.2e-3
 
 Anderson-Darling statistic = A2       :    3.93
 p-value of test no 108                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.61
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.15
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.22
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.82
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.72
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.39
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.67
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 127                :    0.01
 
 Anderson-Darling statistic = A2       :    3.56
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.40
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.74
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.68
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 136                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.29
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17584.38
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.10
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.73
 p-value of test no 147                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.96
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.06
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.78
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.23
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.46
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.80
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.96
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.53
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.99
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.44
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.45
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.51
 p-value of test no 159                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.67
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.15
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.38
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.57
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.70
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.80
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.18
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.56
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5205.81
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.14
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.63
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.39
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.13
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.71
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.50
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.91
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.80
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.76
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.64
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.38
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.00
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.42
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 210                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10003.36
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.35
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.048
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.04
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.36
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.29
 p-value of test no 226                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.97
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4007.73
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11605.49
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.06
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.32
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999927662
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.40
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  8000061024
 
 Normal statistic for number of bits   :    0.48
 p-value of test no 234                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 238                :    0.38
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 247                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.05
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.24
 p-value of test no 253                :    0.11
 
 Sample variance                       :    1.27
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:57.34
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35724
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 17                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 33                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 36                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 40                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 44                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.28
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.52
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.30
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.91
 p-value of test no 49                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.40
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.34
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.59
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.61
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.14
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.81
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.63
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.43
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.14
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.24
 p-value of test no 66                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.35
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.29
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908252
   j =  2                              :            45871
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45831
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869831
   j =  1                              :        399908343
   j =  2                              :            45821
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 86                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 105                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 117                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.092
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.16
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.33
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.47
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.11
 p-value of test no 122                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.57
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.27
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.10
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.99
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.99
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.45
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17149.61
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.24
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.68
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.49
 p-value of test no 149                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.52
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.15
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.57
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.37
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.60
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.11
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.72
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.41
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.49
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.73
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.47
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.52
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.13
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.45
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.53
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.37
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.69
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.19
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.36
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.93
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.05
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.52
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5085.78
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.33
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.16
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.18
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.64
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 183                :    0.74
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.72
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.40
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 202                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.66
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 205                :  8.5e-3
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.33
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10046.13
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9861.18
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.01
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.86
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.29
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.54
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11798.62
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.45
 p-value of test no 230                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.00
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999845108
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999893870
 
 Normal statistic for number of bits   :   -0.84
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 238                :    0.48
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 241                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.95
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:48.10
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35725
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 9                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 11                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5580
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7181
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 22                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 23                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.08
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.21
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.72
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.25
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.59
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.08
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.31
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.77
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.94
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.75
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1368.39
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7238.52
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.35
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.5e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 64                 :  7.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.67
 p-value of test no 65                 :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.95
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.77
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5006.48
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45678
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869678
   j =  1                              :        399908644
   j =  2                              :            45678
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908034
   j =  2                              :            45980
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 88                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 95                 :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 98                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 108                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 112                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.28
 p-value of test no 119                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.13
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.88
 p-value of test no 122                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.21
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.18
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.63
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 128                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.07
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.14
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.56
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.87
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.99
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.74
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.82
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.35
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.94
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.89
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.34
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.65
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.12
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.18
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 155                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.10
 p-value of test no 156                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.57
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.94
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.18
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.07
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.99
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.75
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.82
 p-value of test no 163                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.58
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.43
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.54
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.07
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.08
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.79
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.00
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.61
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.86
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.45
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.71
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.63
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 182                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    1.28
 p-value of test no 184                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.22
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.63
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.79
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.74
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.16
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.20
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 217                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.62
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.12
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.54
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3954.96
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11974.54
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.66
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.72
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000023530
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.64
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999989132
 
 Normal statistic for number of bits   :  -0.086
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.40e-4
 p-value of test no 240                :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 243                :    0.07
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:54.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35726
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1259
 p-value of test no 11                 :    0.9979
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334379
   j =  1                              :        599997482
   j =  2                              :             1259
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4475
 p-value of test no 14                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4404
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 17                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7137
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.48
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 33                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.10
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 42                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.09
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.53
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.92
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.24
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.93
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   81.21
 p-value of test no 51                 :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.95
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.04
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  465.25
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.64
 p-value of test no 56                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7142.89
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 60                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.76
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.82
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.86
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5068.96
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908143
   j =  2                              :            45924
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46187
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870187
   j =  1                              :        399907629
   j =  2                              :            46181
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-4
 p-value of test no 76                 :    0.9991    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 77                 :  3.0e-3
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 78                 :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 103                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.65e-4
 p-value of test no 109                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    3.37
 p-value of test no 111                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.77
 p-value of test no 115                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.56
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.60
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.36
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.25
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.21
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.01
 p-value of test no 123                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.87
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.34
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.98
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.84
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.21
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.48
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17232.13
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.40
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.09
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.79
 p-value of test no 148                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.02
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.22
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.88
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.55
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.24
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.82
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.50
 p-value of test no 156                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.02
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.34
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.11
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.11
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.92
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.58
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.33
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.40
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.24
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.22
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.66
 p-value of test no 167                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.95
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.04
 p-value of test no 169                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.52
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.78
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.12
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5084.80
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.60
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.55
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.09
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.07
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.74
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 180                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.22
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.99
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.80
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9989.52
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    3.92
 p-value of test no 214                :  1.0e-2
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10390.06
 p-value of test no 215                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.33
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.34
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.09
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.44
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.36
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.85
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11965.10
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.98
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000063880
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.47
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999788858
 
 Normal statistic for number of bits   :   -1.67
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.06
 p-value of test no 238                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.48
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 243                :    0.45
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.37
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:07.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35727
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 6                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 10                 :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 14                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    2.37
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.52
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.35
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.25
 p-value of test no 49                 :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.11
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.12
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.82
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.93
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.38
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1463.48
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.06
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.80
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.50
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  150.57
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.79
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908113
   j =  2                              :            45939
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 102                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 3.28e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.31
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.03
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   38.81
 p-value of test no 121                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.35
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.70
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.88
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.43
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.75
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 132                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.29
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.12
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.18
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17595.65
 p-value of test no 145                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.55
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.27
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.57
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.07
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.43
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.53
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.03
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.51
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.27
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.48
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.52
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.42
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.49
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.02
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.39
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.20
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.50
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.53
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.33
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.24
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.70
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4884.85
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.07
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.04
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.79
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.19
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.32
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.32
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.96
 p-value of test no 175                :    0.9943
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.87
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.85
 p-value of test no 177                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.04
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 188                :    0.83
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.26
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 206                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.23
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.64
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.65
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 221                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.97
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.18
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.58
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4199.41
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.80
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.80
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.47
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999917189
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.91
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999969371
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.68
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.16
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.069
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:15.73
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35728
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 6                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 33                 :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.90
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.45
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.32
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.48
 p-value of test no 52                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.38
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.51
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.17
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.99
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.31
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.00
 p-value of test no 65                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.02
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.73
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.97
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908052
   j =  2                              :            45968
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908620
   j =  2                              :            45690
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 90                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 112                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.20
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.21
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.04
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.52
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.75
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.99
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.58
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.25
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.90
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.77
 p-value of test no 135                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.34
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17602.77
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.57
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.97
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.39
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.82
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.81
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.55
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.34
 p-value of test no 152                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.61
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.90
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.91
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.36
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.37
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.53
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.34
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.21
 p-value of test no 161                :  4.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.61
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.34
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.53
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.22
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.99
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.23
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4924.74
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.96
 p-value of test no 169                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.29
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.30
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.82
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.97
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.33
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.42
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.21
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.31
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 191                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.20
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.37
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.52
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.93
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.10
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.24
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4840.32
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.59
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.92
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.02
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.08
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.95
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000024640
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.46
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999999611
 
 Normal statistic for number of bits   : -3.08e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 237                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.73
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.27
 p-value of test no 243                :    0.01
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 248                :    0.49
 
 Sample variance                       :    1.91
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:31.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35729
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 4                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.89
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.18
 p-value of test no 35                 :    0.9940
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9933
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 45                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.90
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.27
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.78
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.05
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.94
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.15
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.88
 p-value of test no 53                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.84
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  373.99
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.97
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6875.85
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.89
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.45
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.47
 p-value of test no 66                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.25
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.64
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45555
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869555
   j =  1                              :        399908892
   j =  2                              :            45551
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908043
   j =  2                              :            45974
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.33
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 108                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.43
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.15
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.04
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.72
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.25
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.15
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.49
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.47
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.45
 p-value of test no 133                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.36
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.91
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  167.36
 p-value of test no 141                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 143                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17346.19
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.45
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.78
 p-value of test no 147                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.38
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.05
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.94
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.18
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.87
 p-value of test no 152                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.88
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.83
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.91
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.76
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.73
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.65
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.68
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.36
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.53
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.17
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.65
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.51
 p-value of test no 164                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.40
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.99
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.68
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.23
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.02
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.35
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.92
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.89
 p-value of test no 172                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5219.54
 p-value of test no 173                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.12
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.73
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.40
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.42
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.61
 p-value of test no 178                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.98
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.13
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 201                :  7.8e-3
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 202                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  250.87
 p-value of test no 203                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.35
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.98
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.62
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9942.83
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.13
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.09
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.39
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.90
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11935.56
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11599.18
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.98
 p-value of test no 231                :    0.92
 
 
 -----------------------------------------------
 Total number of bits:  7999948362
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.50
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000273598
 
 Normal statistic for number of bits   :    2.16
 p-value of test no 234                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 242                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9917
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:39.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35730
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 4                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997173
   j =  2                              :             1412
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5448
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 15                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    3.19
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9956
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.99
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.39
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.97
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.83
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.94
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.15
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.03
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1437.65
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.54
 p-value of test no 57                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.40
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.84
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.93
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.16
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4870.57
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45521
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869521
   j =  1                              :        399908959
   j =  2                              :            45519
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46085
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870085
   j =  1                              :        399907835
   j =  2                              :            46075
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 103                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 110                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.65
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.48
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.87
 p-value of test no 121                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.67
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.97
 p-value of test no 124                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.24
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.86
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.52
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.61
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 136                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.88
 p-value of test no 141                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 142                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17047.61
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.67
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.26
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.95
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.83
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.20
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.35
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.04
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.58
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.43
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.91
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.75
 p-value of test no 157                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.81
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.30
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.05
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.45
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.65
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.57
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.20
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.53
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.54
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.85
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4788.81
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.29
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.19
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.02
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.59
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4849.51
 p-value of test no 173                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.41
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.96
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.32
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.06
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.64
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.45
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.38
 p-value of test no 203                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.43
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9847.01
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.51
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.82
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 225                :    0.9992    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4913.18
 p-value of test no 226                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.10
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.34
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.41
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.97
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.40
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000047773
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.15
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999906905
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:11.28
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35731
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 20                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.94
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.89
 p-value of test no 29                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    2.47
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     643
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    1.92
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.51
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.43
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.84
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.20
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  475.29
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.36
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6984.04
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.23
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.66
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.03
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.99
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.34
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46099
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870099
   j =  1                              :        399907805
   j =  2                              :            46093
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908483
   j =  2                              :            45754
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 78                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 83                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 100                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 116                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.89
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.52
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.07
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.47
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.65
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.34
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.66
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.35
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.34
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.59
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.61
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 144                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17219.12
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.41
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.38
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.56
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.29
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.87
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.88
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.68
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.75
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.88
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.43
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.70
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.80
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.66
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.32
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.37
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.33
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.58
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.78
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.81
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.39
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.69
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.14
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.80
 p-value of test no 170                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.51
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.01
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4951.92
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  452.89
 p-value of test no 174                :  4.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.18
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.030
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.06
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 188                :    0.89
 
 Sample variance                       :    1.07
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 192                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.85
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.88
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 202                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.92
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.65
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.57
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    4.75
 p-value of test no 214                :  4.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9601.03
 p-value of test no 215                :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.056
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.10
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 219                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 221                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.76
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4792.03
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.03
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.43
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.59
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.10
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.34
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999910454
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.29
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999943607
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.12
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:43.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35732
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 26                 :    0.9928
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.87
 p-value of test no 28                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    2.14
 p-value of test no 33                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.47
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.93
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.63
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.73
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.73
 p-value of test no 53                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.81
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.03
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.07
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.02
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.73
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 64                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.64
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.04
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.63
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.69
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45732
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869732
   j =  1                              :        399908538
   j =  2                              :            45728
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908664
   j =  2                              :            45659
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:47.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 78                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 102                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.92
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.64
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.92
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.37
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.19
 p-value of test no 122                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.14
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.73
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.59
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.96
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 134                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 135                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 139                :    0.78
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.64
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17274.70
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.34
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.34
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.54
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.92
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.55
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.42
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.69
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.52
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.84
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.67
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.95
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.45
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.97
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.38
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.33
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.01
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.84
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.40
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.37
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.53
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.95
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.49
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.74
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.94
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.61
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.33
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.71
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.04
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.85
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.90
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.73
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 179                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 192                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.81
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.33
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.17
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.45
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.93
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4783.74
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.11
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4318.01
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.67
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.20
 p-value of test no 229                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.93
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.21
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000043624
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.20
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999946070
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.065
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.80
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 253                :    0.96
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:45.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35733
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5435
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    3.43
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.73
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 35                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.32
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.64
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.81
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.85
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.08
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.02
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.58
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.18
 p-value of test no 55                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.66
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.96
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 60                 :  5.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   57.50
 p-value of test no 61                 :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.33
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.18
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.86
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4985.74
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45829
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869829
   j =  1                              :        399908347
   j =  2                              :            45819
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907840
   j =  2                              :            46071
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 81                 :    0.9933
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.79
 p-value of test no 115                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.50
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.80
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.47
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.52
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.29
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.88
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.88
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.46
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.15
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.27
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 134                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.38
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 140                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.70
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.26
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.34
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.59
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.69
 p-value of test no 148                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.00
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.51
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.17
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.92
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.32
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.48
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.72
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.25
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.47
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.13
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.65
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   48.89
 p-value of test no 160                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.74
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.25
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.23
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.24
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.30
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.41
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.22
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5048.00
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.31
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.49
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.39
 p-value of test no 171                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.12
 p-value of test no 172                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.00
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.12
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.27
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.69
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.57
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.17
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 183                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 184                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.033
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.13
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.38
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.73
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.14
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 204                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.80
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9853.02
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 213                :    0.91
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9720.19
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.17
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.57
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.76
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4146.51
 p-value of test no 228                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.90
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.99
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   32.80
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  7999957869
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.82
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999924680
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 238                :    0.09
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 243                :    0.62
 
 Sample variance                       :    1.68
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 247                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.88
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.89
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 253                :    0.19
 
 Sample variance                       :    1.91
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:03.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35734
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 17                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.08
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.05
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     613
 p-value of test no 31                 :    0.30
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 36                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 38                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.36
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.52
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.67
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.87
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.35
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.64
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.76
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.20
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.34
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.66
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.21
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.66
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.85
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.29
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4902.74
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908633
   j =  2                              :            45676
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45770
 p-value of test no 71                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869770
   j =  1                              :        399908461
   j =  2                              :            45768
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.28
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.01
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.43
 p-value of test no 121                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.06
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.14
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.86
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.17
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.40
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.28
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.93
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.30
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 142                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 144                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.50
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.48
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.68
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.31
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.79
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.24
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.04
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.27
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.67
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.32
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.13
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.54
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.99
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.64
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.13
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.43
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.08
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.73
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.38
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.96
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.32
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5111.29
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.47
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.70
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.03
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.73
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.24
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  432.73
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.08
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.53
 p-value of test no 176                :  9.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.06
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.37
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.43
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.89
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 200                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.01
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.57
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.34
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 212                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9640.09
 p-value of test no 215                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4979.97
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4897.60
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4206.13
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.85
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12095.85
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11433.87
 p-value of test no 230                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.78
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000118993
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.62
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999959420
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.92
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.30
 p-value of test no 253                :    0.99
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:12.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35735
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.47
 p-value of test no 23                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    4.41
 p-value of test no 27                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.50
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     555
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     331
 p-value of test no 37                 :    0.04
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.63
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   42.44
 p-value of test no 48                 :  9.6e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.03
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.48
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.63
 p-value of test no 53                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.15
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.30
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1381.69
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6827.70
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.52
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.46
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.46
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.42
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5184.82
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46089
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870089
   j =  1                              :        399907825
   j =  2                              :            46083
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908056
   j =  2                              :            45966
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 102                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 107                :    0.9913
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.32
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.02
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.27
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.88
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.64
 p-value of test no 123                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.50
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.26
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.81
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.48
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.05
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.79
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 139                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    4.39
 p-value of test no 140                :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  184.62
 p-value of test no 141                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17500.39
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.72
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.55
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.05
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.76
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.56
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.38
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.93
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.54
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.31
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.96
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.39
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.03
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.68
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.25
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.33
 p-value of test no 161                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.25
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.31
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.92
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.67
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.41
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.56
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.03
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.67
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.93
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.92
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.69
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.08
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.57
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.71
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.25
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.42
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.94
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.74
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.17
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.06
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.25
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.84
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.37
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9822.35
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10049.27
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.98
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.01
 p-value of test no 222                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.75
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.13
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.57
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.35
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12031.33
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999929993
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.20
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000009307
 
 Normal statistic for number of bits   :   0.074
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    2.57
 p-value of test no 239                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 243                :    0.79
 
 Sample variance                       :    1.57
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.29
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.44
 p-value of test no 253                :    0.33
 
 Sample variance                       :    1.70
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:54.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  28  SimpPoker, r = 0                9.6e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35736
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 8                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 12                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5282
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 14                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 21                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 32                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    3.24
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.84
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.46
 p-value of test no 49                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.08
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.19
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.90
 p-value of test no 53                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.07
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.91
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.37
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7180.80
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.00
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 64                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.53
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.33
 p-value of test no 66                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.73
 p-value of test no 67                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5177.04
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46008
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870008
   j =  1                              :        399907989
   j =  2                              :            45998
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46351
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870351
   j =  1                              :        399907300
   j =  2                              :            46347
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 99                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 106                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 115                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.24
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 117                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.38
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 120                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.30
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.81
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.39
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.62
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.62
 p-value of test no 125                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.54
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.78
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.78
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.25
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 143                :    0.01
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 144                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17649.28
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.01
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.81
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.13
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.18
 p-value of test no 149                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.02
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.03
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.83
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.44
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.38
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.02
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.51
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.40
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.06
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.58
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.83
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.69
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.99
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.01
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.04
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.04
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.86
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.94
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.68
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.60
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.96
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.45
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.84
 p-value of test no 172                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4978.71
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.51
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.81
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.33
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 181                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 183                :    0.80
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.38
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.31
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.96
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.93
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.05
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.55
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.50
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.34
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.98
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4038.63
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.66
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11919.04
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.72
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999978341
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.42
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999966773
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 237                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 245                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 246                :    0.07
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 247                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 253                :    0.85
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:48.92
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35737
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9975
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 6                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 17                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7112
 p-value of test no 18                 :    0.9922
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7401
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.32
 p-value of test no 22                 :  6.2e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.23
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.55
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.78
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.42
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.74
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.86
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 52                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.34
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  379.09
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.39
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.24
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.41
 p-value of test no 61                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.59
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.89
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.85
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4950.64
 p-value of test no 68                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45953
 p-value of test no 70                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869953
   j =  1                              :        399908097
   j =  2                              :            45947
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45799
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869799
   j =  1                              :        399908406
   j =  2                              :            45791
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 73                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 90                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 92                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 103                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -8.20e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 116                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.18
 p-value of test no 119                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.60
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.66
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.14
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.04
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.79
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.47
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
 p-value of test no 127                :    0.9948
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.53
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.54
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.63
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.59
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.28
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 144                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17314.35
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.93
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.11
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.73
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.09
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.37
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.20
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.94
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.37
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.33
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.56
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.69
 p-value of test no 156                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.31
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.63
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.45
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.90
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.25
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.82
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.95
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.33
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.21
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.52
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.20
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.15
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.69
 p-value of test no 169                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.85
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.98
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.20
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.80
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.43
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.51
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.10
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.46
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 195                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.78
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.48
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.47
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.37
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.99
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.07
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.63
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.27
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.36
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.67
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.66
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11779.78
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.81
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999927611
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.64
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000018526
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.37
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:55.14
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35738
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1245
 p-value of test no 11                 :    0.9994    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334365
   j =  1                              :        599997510
   j =  2                              :             1245
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5541
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 14                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 17                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    3.75
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.31
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.20
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.62
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.28
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.87
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.71
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.46
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.66
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1386.94
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.51
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.37
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.16
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.95
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.30
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.83
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908139
   j =  2                              :            45926
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45766
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869766
   j =  1                              :        399908469
   j =  2                              :            45764
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.15e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
 p-value of test no 113                :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 116                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.43
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.89
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.91
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.93
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.33
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.31
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.66
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.82
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.85
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.56
 p-value of test no 134                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.00
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17626.39
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.52
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.54
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.74
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.92
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.30
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.19
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.40
 p-value of test no 152                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.75
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.77
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.06
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.00
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.65
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.93
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.05
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.13
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.06
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.00
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.80
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.15
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.76
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.54
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.42
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.49
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.41
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.33
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.88
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.24
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.09
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.57
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.13
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.17
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.14
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.76
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 202                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.69
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.24
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.11
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.28
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.24
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4724.23
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.71
 p-value of test no 226                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.76
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.92
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.80
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11788.70
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.38
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999934058
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.53
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999968501
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 243                :    0.33
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35739
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 8                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 11                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4190
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 30                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    3.66
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 40                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.20
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.11
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.55
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.00
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.14
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.35
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.82
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.04
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.07
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6976.35
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 58                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  6.5e-3
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.36
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.89
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.98
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4889.55
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909103
   j =  2                              :            45444
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908030
   j =  2                              :            45976
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 78                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 93                 :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  8.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 100                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 104                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 108                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.16
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.85
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.64
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.78
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.03
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.82
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.92
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.60
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.08
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.59
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17630.37
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.79
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.78
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.06
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.36
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.70
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.50
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.47
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.75
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.79
 p-value of test no 155                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.60
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.26
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.91
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.48
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.55
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.60
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.11
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.64
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.36
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.39
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.44
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.07
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5223.72
 p-value of test no 168                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.10
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.57
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.65
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.92
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.31
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.22
 p-value of test no 174                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.62
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.66
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.36
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 182                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
 p-value of test no 194                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.48
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.27
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.95
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
 p-value of test no 209                :    0.9976
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9665.22
 p-value of test no 211                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.98
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 220                :    0.09
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.16
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.00
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4105.79
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.89
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.63
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.93
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.90
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  7999908447
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.83
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000000340
 
 Normal statistic for number of bits   : 2.69e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 243                :    0.12
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.19
 p-value of test no 248                :    0.12
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 253                :    0.20
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:35.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35740
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 4                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7572
 p-value of test no 15                 :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 19                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 22                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.03
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     953
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.52
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    4.84
 p-value of test no 32                 :  3.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 33                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    3.78
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.59
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:24.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.18
 p-value of test no 46                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.71
 p-value of test no 48                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.14
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.23
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.32
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.87
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.56
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.31
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  368.53
 p-value of test no 55                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.51
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.79
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.56
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.11
 p-value of test no 65                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   95.66
 p-value of test no 67                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5144.42
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46375
 p-value of test no 70                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870375
   j =  1                              :        399907251
   j =  2                              :            46373
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45801
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869801
   j =  1                              :        399908400
   j =  2                              :            45797
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 73                 :  1.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.34
 p-value of test no 74                 :  6.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  7.6e-3
 
 Anderson-Darling statistic = A2       :    3.35
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 81                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 93                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 106                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-3
 p-value of test no 107                :    0.9985
 
 Anderson-Darling statistic = A2       :    5.25
 p-value of test no 108                :  2.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.42
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.72
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.58
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.14
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.26
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.60
 p-value of test no 124                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.88
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.86
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.46
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.95
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.39
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.97
 p-value of test no 141                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17328.47
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.29
 p-value of test no 146                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.97
 p-value of test no 147                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.75
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.09
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.88
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.55
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.96
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.91
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.08
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.15
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 157                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  575.06
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.59
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.95
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.12
 p-value of test no 161                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.59
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.86
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.62
 p-value of test no 166                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.09
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.53
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.53
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.76
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.04
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.73
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.35
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.35
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.25
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.23
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 177                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 185                :  1.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    5.33
 p-value of test no 187                :  2.1e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.13
 p-value of test no 188                :    0.9991    *****
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.20
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.31
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.03
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 204                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.31
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.30
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.15
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.25
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.52
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.78
 p-value of test no 226                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.78
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.78
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12246.81
 p-value of test no 229                :  3.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.26
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.59
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000079456
 
 Normal statistic for number of bits   :    0.63
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.03
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999874286
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    2.15
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.20
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.58
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35741
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 4                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7477
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7124
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    4.74
 p-value of test no 24                 :  3.8e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     957
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 35                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.86
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.62
 p-value of test no 46                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.94
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.72
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.78
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.12
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.17
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.25
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.83
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  473.60
 p-value of test no 55                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1566.05
 p-value of test no 56                 :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6847.41
 p-value of test no 57                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 60                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.20
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.11
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.42
 p-value of test no 66                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.29
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5158.74
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46431
 p-value of test no 70                 :  5.1e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870431
   j =  1                              :        399907143
   j =  2                              :            46421
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45930
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869930
   j =  1                              :        399908144
   j =  2                              :            45922
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 83                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 102                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 113                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.05
 p-value of test no 115                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.84
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.86
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.99
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.84
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.45
 p-value of test no 124                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.75
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.46
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.53
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.41
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 140                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.10
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 144                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.51
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.26
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.18
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.01
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.90
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   40.49
 p-value of test no 150                :  1.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.71
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   58.78
 p-value of test no 152                :  7.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.79
 p-value of test no 153                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.41
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.00
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.70
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.51
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.32
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.12
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.20
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.21
 p-value of test no 162                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.19
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.80
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.59
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.91
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.08
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.80
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.62
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.62
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.96
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.07
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.33
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  338.92
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.65
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.47
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.49
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.72
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.94
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.37
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.58
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.94
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 210                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.05
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 213                :    0.84
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9883.16
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.97
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.93
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3997.53
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.79
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.29
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12059.19
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.94
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000041605
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.24
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999991634
 
 Normal statistic for number of bits   :  -0.066
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 235                :  1.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 236                :    0.9950
 
 Anderson-Darling statistic = A2       :    8.47
 p-value of test no 237                :  7.7e-5    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -4.09
 p-value of test no 238                : 1 -  2.1e-5    *****
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 240                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:19.36
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0              1 -  2.1e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35742
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1472
 p-value of test no 5                  :  2.0e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334592
   j =  1                              :        599997057
   j =  2                              :             1470
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 11                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5422
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 14                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 21                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 28                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.57
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.17
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.33
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.16
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.41
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.27
 p-value of test no 50                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.63
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.78
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.39
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.86
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.14
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.28
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 58                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.44
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 64                 :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.54
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.85
 p-value of test no 66                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.73
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5082.33
 p-value of test no 68                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908375
   j =  2                              :            45805
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46044
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870044
   j =  1                              :        399907919
   j =  2                              :            46030
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 73                 :    0.9913
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.32
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.69
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.88
 p-value of test no 121                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.61
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.42
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.88
 p-value of test no 125                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.06
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.60
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.83
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.12
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.30
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17370.97
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.22
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.25
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.60
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.85
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.81
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.26
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.56
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.07
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.70
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.74
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.39
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.03
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.35
 p-value of test no 158                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.34
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.24
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.86
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.09
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.30
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.72
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.65
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.24
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4845.24
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.45
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.48
 p-value of test no 170                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.06
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.98
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.81
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.18
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.84
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.59
 p-value of test no 176                :    0.99
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.02
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.72
 p-value of test no 196                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.93
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.08
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 209                :    0.9924
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.94
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9793.74
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4751.96
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 224                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.37
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4251.93
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.93
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.44
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.37
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.74
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  7999996320
 
 Normal statistic for number of bits   :  -0.029
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.10
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999993725
 
 Normal statistic for number of bits   :  -0.050
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
 p-value of test no 236                :    0.9940
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 238                :    0.97
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:52.09
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35743
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 8                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5420
 p-value of test no 13                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 18                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.15
 p-value of test no 22                 :    0.9989
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.19
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.23
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.19
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.72
 p-value of test no 50                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.74
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.20
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.25
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  383.06
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.66
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.64
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.90
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.49
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.52
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.09
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4910.22
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45855
 p-value of test no 70                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869855
   j =  1                              :        399908294
   j =  2                              :            45847
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45802
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869802
   j =  1                              :        399908399
   j =  2                              :            45796
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 79                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 98                 :  9.3e-4    *****
 
 Anderson-Darling statistic = A2       :    5.04
 p-value of test no 99                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 117                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.72
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.59
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.38
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.75
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.86
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.19
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.95
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.02
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.94
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.69
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 139                :  5.0e-4    *****
 
 Anderson-Darling statistic = A2       :    5.33
 p-value of test no 140                :  2.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  181.28
 p-value of test no 141                :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 142                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17780.66
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.40
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.08
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.97
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.97
 p-value of test no 149                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.46
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.61
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.25
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.43
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.28
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.42
 p-value of test no 155                :  4.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.84
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.19
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.24
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  188.61
 p-value of test no 159                :  1.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.48
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.45
 p-value of test no 161                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.59
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.04
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.85
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.11
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.32
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.34
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4961.64
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.82
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.04
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.77
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.06
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4930.07
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.05
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.38
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.05
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.11
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.000
 p-value of test no 183                :    0.50
 
 Sample variance                       :    0.31
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
 p-value of test no 194                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.46
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.81
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.87
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10202.27
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 214                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9826.71
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.30
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4699.72
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.45
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.02
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11426.30
 p-value of test no 229                :    0.9956
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.52
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.24
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999902387
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 232                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.08
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999913457
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 234                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 235                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.69
 p-value of test no 238                :  3.5e-3
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 248                :    0.74
 
 Sample variance                       :    2.46
 p-value of test no 249                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 252                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35744
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 8                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    2.66
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     524
 p-value of test no 31                 :    0.9992    *****
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     278
 p-value of test no 37                 :    0.89
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 42                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.91
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.53
 p-value of test no 47                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.13
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.38
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.90
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.94
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.12
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.82
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.12
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  508.81
 p-value of test no 55                 :  7.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.94
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.07
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.14
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.27
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.92
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.63
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5187.63
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45690
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869690
   j =  1                              :        399908621
   j =  2                              :            45688
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907863
   j =  2                              :            46058
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 81                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 102                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.81
 p-value of test no 119                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.11
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.27
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.71
 p-value of test no 123                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.09
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.99
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 128                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.40
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.66
 p-value of test no 133                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.46
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.53
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.88
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.39
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17276.59
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.63
 p-value of test no 146                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.79
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.46
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.21
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.04
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.67
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.23
 p-value of test no 154                :  3.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.85
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.91
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.31
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.56
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.09
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.79
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.45
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.28
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  428.95
 p-value of test no 163                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.44
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.79
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.07
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.27
 p-value of test no 167                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.67
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.17
 p-value of test no 169                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.83
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.58
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.43
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.40
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.76
 p-value of test no 174                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.63
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.60
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.39
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.99
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.20
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.14
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.96
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.86
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10323.32
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.14
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.96
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.70
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.24
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12040.76
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.27
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.53
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000001399
 
 Normal statistic for number of bits   :   0.011
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.19
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999894776
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 234                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.36
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.73
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:58.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NJumps, t = 5        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35745
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 8                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5458
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4352
 p-value of test no 14                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7138
 p-value of test no 20                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    1.73
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.79
 p-value of test no 28                 :  3.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 30                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 38                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.47
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.62
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.65
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.48
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.68
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.80
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.83
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.57
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6756.66
 p-value of test no 57                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.61
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 64                 :  8.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   89.91
 p-value of test no 65                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.53
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.06
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5027.04
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45607
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869607
   j =  1                              :        399908790
   j =  2                              :            45599
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46276
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870276
   j =  1                              :        399907455
   j =  2                              :            46262
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 83                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.78e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.61
 p-value of test no 116                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.03
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.29
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.78
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 123                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.04
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.97
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.92
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.99
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 135                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.32
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17327.21
 p-value of test no 145                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.48
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.15
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.87
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.96
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.27
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 152                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.15
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.94
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.60
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.82
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.35
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.07
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.55
 p-value of test no 159                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.78
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.83
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.30
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.64
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.71
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.63
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.20
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.52
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.64
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.52
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.21
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.87
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.67
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.54
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  437.04
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.23
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.62
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 192                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
 p-value of test no 194                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.12
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.95
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.11
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.81
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.47
 p-value of test no 211                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.18
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.84
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4970.25
 p-value of test no 226                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.91
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.63
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12084.78
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11565.58
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.98
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  8000064438
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.02
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000081142
 
 Normal statistic for number of bits   :    0.64
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.68
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 253                :    0.89
 
 Sample variance                       :    2.01
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35746
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 3                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 9                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 14                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 24                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    3.40
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     248
 p-value of test no 37                 :    0.9989
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.64
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.41
 p-value of test no 47                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.42
 p-value of test no 48                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.47
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.56
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.40
 p-value of test no 52                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.02
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.84
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.86
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1481.08
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.03
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.99
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.82
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.45
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.97
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5323.25
 p-value of test no 68                 :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908451
   j =  2                              :            45764
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45871
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869871
   j =  1                              :        399908262
   j =  2                              :            45863
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  5.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 104                :    0.9900
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 105                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.01
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.36
 p-value of test no 120                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.10
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.46
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.41
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.25
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.25
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.63
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.34
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.50
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.79
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17390.54
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.05
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.52
 p-value of test no 148                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.80
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.76
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.34
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.69
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.64
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.78
 p-value of test no 155                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.28
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.79
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.59
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.63
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.10
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.33
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.58
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.50
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.69
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.06
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.72
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.25
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.22
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.39
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.06
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.91
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.43
 p-value of test no 172                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.88
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.75
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.74
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.22
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.91
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.07
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.04
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 201                :    0.02
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.51
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 204                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.71
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.62
 p-value of test no 211                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10107.09
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.96
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.00
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.48
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.84
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.97
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11805.85
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.29
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000153010
 
 Normal statistic for number of bits   :    1.21
 p-value of test no 232                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.79
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999907130
 
 Normal statistic for number of bits   :   -0.73
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.12
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 248                :    0.98
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 253                :    0.65
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:15.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35747
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 4                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4239
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 19                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9901
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.66
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.59
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.06
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.35
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.57
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.78
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.92
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.88
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.92
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.34
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7100.10
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 59                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.79
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.17
 p-value of test no 65                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.94
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.96
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5073.76
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45976
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869976
   j =  1                              :        399908054
   j =  2                              :            45964
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46055
 p-value of test no 71                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870055
   j =  1                              :        399907895
   j =  2                              :            46045
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 76                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.09
 p-value of test no 116                :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.42
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.13
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.78
 p-value of test no 121                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.28
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.69
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.58
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.44
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.00
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.58
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.34
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.30
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17582.60
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.60
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.93
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.25
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.77
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.88
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.47
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.38
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.21
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.71
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.25
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.08
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.00
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.12
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.10
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.12
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.19
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.61
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.91
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.91
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4996.01
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.09
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.13
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.89
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.27
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.34
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.86
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.08
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.70
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.039
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.61
 p-value of test no 178                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 179                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.48
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.74
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.03
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.76
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10130.47
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.41
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4714.57
 p-value of test no 222                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.43
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.93
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3995.37
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11843.00
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.65
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.60
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999964727
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999969191
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.23
 p-value of test no 249                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.78
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:55.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35748
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1256
 p-value of test no 9                  :    0.9984
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334376
   j =  1                              :        599997488
   j =  2                              :             1256
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 11                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1465
 p-value of test no 12                 :  3.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334585
   j =  1                              :        599997070
   j =  2                              :             1465
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 14                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 18                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7473
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 38                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.37
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.56
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.40
 p-value of test no 48                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.66
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.81
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.80
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.98
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.20
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.24
 p-value of test no 56                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.45
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 60                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.70
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.66
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.32
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.25
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.30
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908810
   j =  2                              :            45595
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908290
   j =  2                              :            45846
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 94                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 103                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  6.5e-3
 
 Anderson-Darling statistic = A2       :    3.11
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.09e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 118                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.15
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.77
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.71
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.87
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.44
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.00
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.04
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.01
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.05
 p-value of test no 134                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.70
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 144                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17564.92
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.08
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.25
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.32
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.70
 p-value of test no 149                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.95
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.10
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.10
 p-value of test no 153                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.09
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.83
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.91
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.75
 p-value of test no 158                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.84
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.26
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.50
 p-value of test no 161                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  114.34
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.03
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.38
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.51
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.68
 p-value of test no 166                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.32
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.72
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.71
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.43
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.81
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.16
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5119.55
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.83
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.23
 p-value of test no 175                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.35
 p-value of test no 176                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.30
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 183                :    0.66
 
 Sample variance                       :    1.26
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 193                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.07
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.56
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.14
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.29
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.01
 p-value of test no 211                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.40
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 217                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.32
 p-value of test no 222                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.45
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.05
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.69
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.59
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11560.49
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.68
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  8000021346
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.47
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999902309
 
 Normal statistic for number of bits   :   -0.77
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 238                :    0.74
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 248                :    0.68
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    0.85
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:27.97
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35749
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 5                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5289
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 15                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 33                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 44                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.80
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.60
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.75
 p-value of test no 49                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.95
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.49
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.41
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.85
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.74
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6756.31
 p-value of test no 57                 :    0.9932
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.95
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.84
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.25
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.97
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46102
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870102
   j =  1                              :        399907798
   j =  2                              :            46098
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45786
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869786
   j =  1                              :        399908432
   j =  2                              :            45778
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
 p-value of test no 80                 :    0.9957
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 81                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 94                 :    0.9913
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 101                :    0.79
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 104                :    0.78
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.12
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.77
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.22
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.80
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.58
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.33
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.50
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.17
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   14.73
 p-value of test no 134                :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.49
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.28
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17208.44
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.00
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.05
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.17
 p-value of test no 150                :  4.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.24
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.18
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.05
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.64
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.15
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.67
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.99
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.30
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.03
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.40
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.42
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.24
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.11
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.94
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.07
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.19
 p-value of test no 166                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.20
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.43
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.49
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.80
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.56
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.40
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5121.54
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.07
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.99
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.38
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.66
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.48
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.73
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.18
 p-value of test no 188                :    0.01
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.22
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.22
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.75
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.36
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9801.46
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.60
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.71
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.23
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.51
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.42
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11906.50
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11697.01
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.58
 p-value of test no 231                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999969278
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.93
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  7999889790
 
 Normal statistic for number of bits   :   -0.87
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.25
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.076
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:48.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35750
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 9                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5447
 p-value of test no 13                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7160
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.72
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     860
 p-value of test no 25                 :    0.91
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 26                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 33                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 42                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     125
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.68
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.67
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.96
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.47
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.14
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.89
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   82.08
 p-value of test no 53                 :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  192.60
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.35
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1329.18
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7072.22
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.67
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.84
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.70
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5255.93
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45444
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869444
   j =  1                              :        399909116
   j =  2                              :            45436
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46121
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870121
   j =  1                              :        399907759
   j =  2                              :            46119
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 117                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.87
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.50
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.47
 p-value of test no 120                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.38
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.91
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.07
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.00
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.31
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.73
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.04
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.57
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.43
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.03
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 143                :  9.7e-3
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.58
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.53
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.59
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.21
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.34
 p-value of test no 149                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.83
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.00
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.54
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.58
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.38
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.18
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.47
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.07
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.04
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.80
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.49
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.84
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.41
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.10
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.84
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.36
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.97
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4963.91
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.94
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.28
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.33
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.39
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.11
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.37
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.16
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.25
 p-value of test no 176                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.76
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 188                :    0.56
 
 Sample variance                       :    1.25
 p-value of test no 189                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.18
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.48
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.71
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.21
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.81
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.28
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10146.04
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 217                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.71
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.51
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.33
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.68
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.49
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12078.59
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.94
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.65
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999948014
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.03
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000094639
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 243                :    0.18
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35751
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1457
 p-value of test no 9                  :  6.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334577
   j =  1                              :        599997086
   j =  2                              :             1457
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 11                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 15                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 29                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    3.60
 p-value of test no 33                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.86
 p-value of test no 35                 :  3.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    4.73
 p-value of test no 38                 :  3.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.59
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.46
 p-value of test no 48                 :  8.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.57
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.22
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.39
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.32
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.33
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1393.57
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7167.14
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.09
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.62
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.14
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.41
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.96
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45967
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869967
   j =  1                              :        399908070
   j =  2                              :            45959
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45769
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869769
   j =  1                              :        399908466
   j =  2                              :            45761
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 80                 :    0.9957
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9978
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
 p-value of test no 86                 :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 87                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  3.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.84
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.57
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 106                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 107                :  9.5e-3
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.46
 p-value of test no 116                :    0.9997    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.20
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.50
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.12
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.69
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.48
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.42
 p-value of test no 125                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.19
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 131                :    0.05
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 132                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.37
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.70
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.63
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.58
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.65
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.56
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.98
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.27
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.13
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.95
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.80
 p-value of test no 153                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.29
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.94
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 156                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.47
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.94
 p-value of test no 158                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.00
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.43
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.50
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.07
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.85
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.49
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.24
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.52
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.34
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.54
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.13
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.33
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  326.39
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.34
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.04
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.84
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.09
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.92
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.38
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.71
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.90
 p-value of test no 203                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 204                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 205                : 1 -  7.1e-5    *****
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 206                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.23
 p-value of test no 207                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.44
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.26
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.60
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.06
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.13
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.52
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3998.46
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.48
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.93
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.89
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000019597
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.14
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000111802
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 234                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 243                :    0.97
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35752
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 9                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1279
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334399
   j =  1                              :        599997442
   j =  2                              :             1279
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 12                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7152
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 39                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.71
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.84
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.61
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.47
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.35
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.56
 p-value of test no 53                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.57
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.26
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.12
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.57
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.60
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.78
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.08
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.08
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5017.97
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45901
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869901
   j =  1                              :        399908200
   j =  2                              :            45897
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 74                 :    0.9940
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 109                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.51e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.044
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.07
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 120                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.79
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.68
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.11
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.63
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.59
 p-value of test no 129                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.19
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.82
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 144                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17402.31
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.68
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.65
 p-value of test no 147                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.67
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.44
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.97
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.33
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.06
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.08
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.88
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.58
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.23
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.61
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.76
 p-value of test no 158                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.14
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.56
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.68
 p-value of test no 161                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.50
 p-value of test no 163                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.24
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.42
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.98
 p-value of test no 166                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.00
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.72
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.43
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.49
 p-value of test no 170                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.42
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.32
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.25
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.42
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.38
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.36
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.41
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.62
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.26
 p-value of test no 189                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 192                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.45
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.61
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 206                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.09
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9816.35
 p-value of test no 211                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 214                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9762.77
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 218                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.05
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.39
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.98
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.40
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12036.54
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.78
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.78
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999951158
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.34
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999873044
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 238                :    0.87
 
 Sample variance                       :   0.090
 p-value of test no 239                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 243                :    0.92
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 252                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:30.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35753
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4269
 p-value of test no 14                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 22                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    3.28
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 29                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     321
 p-value of test no 37                 :    0.12
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    3.17
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.07
 p-value of test no 47                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.16
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.15
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.96
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.37
 p-value of test no 52                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.38
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.99
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.92
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.29
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.23
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.98
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.54
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.89
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.97
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46086
 p-value of test no 71                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870086
   j =  1                              :        399907830
   j =  2                              :            46082
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 114                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.11
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.48
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.20
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.46
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.47
 p-value of test no 124                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.86
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.57
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.48
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.26
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.52
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.54
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.69
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17446.37
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.73
 p-value of test no 146                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.09
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.31
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.63
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.00
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.85
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.96
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.30
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.41
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.17
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.33
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.50
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.07
 p-value of test no 161                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.18
 p-value of test no 162                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.85
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.85
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.15
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.04
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.39
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.71
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.82
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.15
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.11
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.12
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.97
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.40
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.41
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.043
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.90
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.055
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.42
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 194                :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.23
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.28
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.26
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.80
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 210                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.34
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.88
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.51
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.75
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4099.87
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.80
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.82
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.63
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.42
 p-value of test no 231                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  8000128506
 
 Normal statistic for number of bits   :    1.02
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.18
 p-value of test no 233                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000065464
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.75
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.18
 p-value of test no 249                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:03.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35754
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 3                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 8                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1265
 p-value of test no 11                 :    0.9966
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334385
   j =  1                              :        599997470
   j =  2                              :             1265
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 14                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 15                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 24                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.22
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.95
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.96
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.77
 p-value of test no 50                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.81
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.20
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.27
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.75
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1533.31
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6991.20
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.01
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.49
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.76
 p-value of test no 67                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.52
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908335
   j =  2                              :            45828
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908066
   j =  2                              :            45964
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 98                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.01e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.22
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.14
 p-value of test no 120                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.73
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.10
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.14
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.22
 p-value of test no 125                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.91
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.14
 p-value of test no 134                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.18
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 140                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.98
 p-value of test no 141                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.38
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.23
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.39
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.58
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.03
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.80
 p-value of test no 150                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.13
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.19
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.64
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.49
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.92
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.43
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.40
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  101.35
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.51
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.98
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  109.36
 p-value of test no 162                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  438.07
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.83
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.85
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.24
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.40
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.75
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.85
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.40
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.80
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.66
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4969.45
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.07
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.79
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.99
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.53
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.01
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 192                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.87
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.01
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.52
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.83
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.41
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 221                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.17
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5004.49
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.75
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.35
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.82
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11740.63
 p-value of test no 230                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.80
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000000241
 
 Normal statistic for number of bits   : 1.91e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.03
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  7999989591
 
 Normal statistic for number of bits   :  -0.082
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  7.5e-3
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 243                :    0.65
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 253                :    0.04
 
 Sample variance                       :    2.18
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:20.14
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35755
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 9                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1263
 p-value of test no 10                 :    0.9971
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334383
   j =  1                              :        599997474
   j =  2                              :             1263
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 11                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 23                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    3.94
 p-value of test no 38                 :  9.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 40                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 42                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.41
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.54
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.07
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.08
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.06
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.97
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  355.72
 p-value of test no 55                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.50
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.55
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.04
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.61
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.35
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.90
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4959.67
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45984
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869984
   j =  1                              :        399908033
   j =  2                              :            45982
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45882
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869882
   j =  1                              :        399908241
   j =  2                              :            45872
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
 p-value of test no 83                 :    0.9918
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 1.38e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.07
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.18
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.05
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.07
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.14
 p-value of test no 125                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.42
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.74
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.35
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.68
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17306.55
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.50
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.68
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.85
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.20
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.52
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.10
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.88
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.94
 p-value of test no 153                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.86
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.62
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.37
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.17
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.85
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.77
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.68
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.27
 p-value of test no 162                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.20
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.13
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.12
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.99
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.58
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4950.18
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  323.12
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.12
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.08
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.05
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.69
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.60
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.46
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.76
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.09
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 192                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.11
 p-value of test no 196                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.20
 p-value of test no 198                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.37
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 205                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.44
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10069.03
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10162.56
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.86
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4698.42
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.42
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4226.00
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11754.02
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.77
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.83
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999959654
 
 Normal statistic for number of bits   :   -0.32
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.63
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999951665
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.69
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 248                :    0.28
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:26.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35756
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7175
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 32                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.06
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.61
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.91
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.47
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.72
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.06
 p-value of test no 51                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.42
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.43
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.85
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.44
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.00
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7008.79
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 60                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.05
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.55
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.85
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.21
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5002.22
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907876
   j =  2                              :            46056
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908474
   j =  2                              :            45763
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 95                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  4.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 99                 :  6.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.46
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.36
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.11
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.91
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.81
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.10
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.12
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.29
 p-value of test no 129                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.45
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.45
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 140                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.33
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17112.46
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.80
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.91
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.47
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.71
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.98
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   57.04
 p-value of test no 151                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.07
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.41
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.91
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.56
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.83
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.01
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.83
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.56
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.24
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.85
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.61
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.24
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.35
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.41
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.01
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.27
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.14
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.39
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.59
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.93
 p-value of test no 171                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  315.93
 p-value of test no 172                :    0.9953
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.30
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.85
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.74
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.07
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.37
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.76
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.65
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
 p-value of test no 200                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.15
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.66
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.37
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.21
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 216                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.18
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.75
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
 p-value of test no 224                :    0.9926
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 225                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4697.03
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.10
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4325.31
 p-value of test no 228                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11873.93
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.10
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.94
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999914480
 
 Normal statistic for number of bits   :   -0.68
 p-value of test no 232                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.74
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000018715
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.61
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:47.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35757
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 15                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 21                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 28                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.42
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.12
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    3.87
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.27
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.91
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.64
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.70
 p-value of test no 50                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.69
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.83
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.29
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  443.61
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1328.67
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.24
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 59                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.69
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.15
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.48
 p-value of test no 66                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.11
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4965.54
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908150
   j =  2                              :            45916
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45815
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869815
   j =  1                              :        399908372
   j =  2                              :            45811
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 91                 :  1.9e-3
 
 Anderson-Darling statistic = A2       :    5.82
 p-value of test no 92                 :  1.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 105                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 111                :    0.9999    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 112                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 114                :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.91
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.21
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.92
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.81
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.12
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.58
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.57
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.33
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.34
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.90
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.70
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17409.57
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.26
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.72
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.34
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.05
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.38
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.40
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.40
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.09
 p-value of test no 153                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.36
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.63
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.60
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.14
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.31
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.85
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.61
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.17
 p-value of test no 161                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.88
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.71
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.06
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.17
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.92
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.02
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.52
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.14
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.91
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.17
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.29
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.46
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.02
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.24
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.08
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.30
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.16
 p-value of test no 189                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 195                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.88
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.56
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.27
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9844.74
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9829.32
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.50
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 223                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.50
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.45
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.02
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.88
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.28
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.43
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999999089
 
 Normal statistic for number of bits   : -7.20e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.18
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999881630
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 234                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.050
 p-value of test no 253                :    0.48
 
 Sample variance                       :    3.02
 p-value of test no 254                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:27.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  53  SampleMean, r = 0               0.9999 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35758
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 7                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 9                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1295
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334415
   j =  1                              :        599997410
   j =  2                              :             1295
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 20                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7142
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 33                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 35                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.07
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.93
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.16
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.01
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.50
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.35
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.46
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.78
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.43
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1529.56
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.26
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.03
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.47
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   17.93
 p-value of test no 66                 :  3.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.68
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.90
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46006
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870006
   j =  1                              :        399907989
   j =  2                              :            46004
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908565
   j =  2                              :            45713
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
 p-value of test no 80                 :    0.9961
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 85                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 94                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 105                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.21e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.39
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.35
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.97
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.62
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.43
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.42
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.69
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.29
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.81
 p-value of test no 136                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.84
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17294.37
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.70
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.96
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.02
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.84
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.03
 p-value of test no 150                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.22
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.49
 p-value of test no 152                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.05
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.37
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.11
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.65
 p-value of test no 157                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.37
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.42
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.26
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.99
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.52
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.31
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.97
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.04
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.17
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  480.57
 p-value of test no 167                :  5.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4800.87
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.95
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.17
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.45
 p-value of test no 171                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.11
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.52
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.77
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.37
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.72
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.75
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.97
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    1.17
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.74
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.88
 p-value of test no 198                :    0.55
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 201                :    0.82
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.59
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.89
 p-value of test no 207                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 210                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9716.11
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 213                :  7.1e-4    *****
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 214                :  5.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10302.27
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.69
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.46
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.27
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.17
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.25
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.55
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11718.83
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.52
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999819968
 
 Normal statistic for number of bits   :   -1.42
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.36
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999952535
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
 p-value of test no 235                :    0.9915
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 238                :    0.01
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 242                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 243                :    0.44
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:22.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 M (L=10000, r=0)    5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35759
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 7                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 16                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7260
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 45                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.26
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.81
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.31
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.55
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.26
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.48
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.27
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.14
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.18
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.97
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.57
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.19
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.25
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.07
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  149.47
 p-value of test no 67                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5018.89
 p-value of test no 68                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907758
   j =  2                              :            46112
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45706
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869706
   j =  1                              :        399908594
   j =  2                              :            45694
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.26e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.046
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.32
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.58
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.78
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.62
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.11
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.57
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.54
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.59
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.60
 p-value of test no 134                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.58
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.25
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.11
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.25
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.60
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.59
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.46
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.06
 p-value of test no 151                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.86
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.40
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.07
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   34.06
 p-value of test no 155                :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.08
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.83
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.34
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.26
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.89
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.42
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.31
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.23
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.32
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.29
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.30
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.94
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5080.83
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.09
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.50
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.26
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5006.35
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.82
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.90
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.11
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.34
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.41
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-4
 p-value of test no 190                :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 191                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.78
 p-value of test no 196                :    0.67
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.81
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.22
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.56
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10151.74
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.37
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.79
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5054.10
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.61
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3987.93
 p-value of test no 228                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11674.82
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.37
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.82
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  7999955700
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.27
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999795398
 
 Normal statistic for number of bits   :   -1.62
 p-value of test no 234                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 238                :    0.11
 
 Sample variance                       :    1.34
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.87
 p-value of test no 244                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 253                :    0.70
 
 Sample variance                       :    2.24
 p-value of test no 254                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:23.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35760
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1464
 p-value of test no 11                 :  3.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334584
   j =  1                              :        599997072
   j =  2                              :             1464
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 12                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4412
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4237
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 45                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.72
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.84
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.05
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.27
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.08
 p-value of test no 51                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.18
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.38
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.91
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  478.92
 p-value of test no 55                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.07
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7147.74
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.58
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.28
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.54
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.83
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.50
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908294
   j =  2                              :            45850
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908492
   j =  2                              :            45754
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 79                 :  4.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.50
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 109                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 110                :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 114                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 116                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.12
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.70
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.94
 p-value of test no 122                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.68
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.80
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.36
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.15
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.60
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.61
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.27
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17414.19
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.05
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.44
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.15
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.60
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.27
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.56
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.49
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.05
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.56
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.75
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.20
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.57
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.96
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.04
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.84
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.04
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.44
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.43
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.94
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.34
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.41
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.25
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.08
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.07
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.08
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.78
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.69
 p-value of test no 179                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 183                :    0.74
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 186                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.24
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.66
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.44
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.12
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 202                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.42
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.89
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10037.14
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.61
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.50
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.64
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.21
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.07
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.96
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11711.65
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.29
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999946310
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.37
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999962834
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:16.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35761
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 6                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:29.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:21.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 9                  :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7480
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 21                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    2.29
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 42                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.98
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.86
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.27
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.40
 p-value of test no 49                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.75
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.49
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.04
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.94
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.33
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.32
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.56
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.59
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.66
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.65
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.70
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908030
   j =  2                              :            45979
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45760
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869760
   j =  1                              :        399908483
   j =  2                              :            45754
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 85                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.41
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 111                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.53
 p-value of test no 116                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.95
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.78
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 121                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.21
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.70
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.93
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.86
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.87
 p-value of test no 133                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.83
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.13
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.61
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17383.57
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.71
 p-value of test no 146                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.96
 p-value of test no 147                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.33
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.71
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.94
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.15
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.03
 p-value of test no 153                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.67
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.63
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.55
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.53
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.77
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.23
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.78
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.64
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.03
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.13
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.63
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.59
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.61
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.95
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.14
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.50
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.52
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.56
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.61
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.12
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  219.64
 p-value of test no 175                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.36
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.37
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    0.29
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 186                :    0.99
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.72
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.54
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.22
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.53
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
 p-value of test no 209                :    0.9978
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9670.20
 p-value of test no 211                :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.18
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4901.75
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.83
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.88
 p-value of test no 227                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.70
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12165.62
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.02
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.53
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999974348
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.23
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000065422
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 238                :    0.35
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.22
 p-value of test no 254                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:48.54
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35762
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 11                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7167
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 16                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 17                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 18                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 20                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 32                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.47
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.04
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.52
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.75
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.05
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.18
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.74
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.92
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.81
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 60                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.46
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 64                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.19
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.27
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  146.86
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5010.14
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908135
   j =  2                              :            45931
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46172
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870172
   j =  1                              :        399907659
   j =  2                              :            46166
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 117                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.13
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.05
 p-value of test no 120                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.66
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.06
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.74
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.84
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.08
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 126                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   22.09
 p-value of test no 129                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.44
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.32
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 140                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   97.37
 p-value of test no 141                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17159.67
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.06
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.86
 p-value of test no 147                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.37
 p-value of test no 148                :    0.9909
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.32
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.25
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.26
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.25
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.30
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.91
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.80
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.05
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.31
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.49
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.11
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  107.87
 p-value of test no 160                :  6.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.18
 p-value of test no 161                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.53
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.21
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.19
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.35
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.23
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.33
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.91
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.52
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.38
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.38
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.66
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4672.40
 p-value of test no 173                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.26
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.56
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.63
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.50
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.30
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 187                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 194                :    0.55
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.62
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.24
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.93
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 214                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.92
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.15
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.98
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.18
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.32
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.36
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11520.41
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.98
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.67
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000216235
 
 Normal statistic for number of bits   :    1.71
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.76
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  7999846203
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 234                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:32.63
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  79  RandomWalk1 J (L=10000, r=15)   0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35763
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 4                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 9                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7514
 p-value of test no 20                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 26                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.07
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 32                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.82
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 40                 :    0.9962
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.48
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.71
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.32
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.88
 p-value of test no 51                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.59
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.73
 p-value of test no 53                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.79
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.17
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1442.29
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7296.82
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.64
 p-value of test no 58                 :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    5.13
 p-value of test no 60                 :  2.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.14
 p-value of test no 61                 :    0.9984
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.79
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.87
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.08
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.99
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45639
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869639
   j =  1                              :        399908724
   j =  2                              :            45635
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45883
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869883
   j =  1                              :        399908240
   j =  2                              :            45871
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
 p-value of test no 72                 :    0.9923
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 74                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 103                :  2.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    3.10
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 4.37e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
 p-value of test no 113                :    0.08
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.27
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.45
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.10
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.17
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.38
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.21
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.94
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.60
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.97
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.75
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.25
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.94
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.43
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.56
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.70
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.59
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.99
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.21
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.21
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.76
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.51
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.93
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.15
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.92
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.63
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.60
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.86
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.87
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.44
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.40
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.27
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.48
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.91
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.36
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.22
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.84
 p-value of test no 173                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.46
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.54
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.38
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.58
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.40
 p-value of test no 179                :  8.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 183                :    0.87
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.24
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.56
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.06
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.67
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.89
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.90
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 221                :    0.9991    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.50
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4780.30
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.42
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3906.94
 p-value of test no 228                :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11833.30
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12018.35
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.21
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999939869
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   76.47
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  7999891017
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.047
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 250                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 252                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:18.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35764
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 5                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 10                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 11                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 12                 :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 17                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7207
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 20                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.14
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.86
 p-value of test no 40                 :  3.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.76
 p-value of test no 46                 :    0.9978
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.02
 p-value of test no 47                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.59
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.10
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.54
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.88
 p-value of test no 51                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.10
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.46
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.01
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1379.66
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7027.33
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.67
 p-value of test no 59                 :  5.1e-3
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 60                 :  5.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   56.21
 p-value of test no 61                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.91
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.60
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.20
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.22
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45835
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869835
   j =  1                              :        399908331
   j =  2                              :            45833
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45715
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869715
   j =  1                              :        399908571
   j =  2                              :            45713
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
 p-value of test no 84                 :    0.9940
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 88                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 95                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 104                :    0.88
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 109                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.83e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 116                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 117                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 118                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.04
 p-value of test no 119                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.10
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.38
 p-value of test no 122                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.90
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.82
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.58
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.29
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.09
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.70
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.31
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.47
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17466.21
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.50
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.06
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.89
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.74
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.40
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.31
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.77
 p-value of test no 152                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.41
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.00
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.79
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.12
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.46
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.59
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.40
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.84
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.18
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.29
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.03
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.05
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.36
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  332.97
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5074.95
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.65
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.05
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.14
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.30
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.94
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.33
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.98
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.54
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 177                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.27
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.65
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.47
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.83
 p-value of test no 184                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.59
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 200                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.22
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 205                :    0.05
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 206                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.59
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.71
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.88
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.07
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.16
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 225                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.87
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4323.91
 p-value of test no 227                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.90
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12047.62
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11483.50
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.63
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999943385
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.38
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000085123
 
 Normal statistic for number of bits   :    0.67
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 250                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.13
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:36.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35765
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 3                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1471
 p-value of test no 12                 :  2.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334591
   j =  1                              :        599997058
   j =  2                              :             1471
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4473
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.86
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    3.35
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.97
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.89
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.99
 p-value of test no 38                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 45                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.34
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.97
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.07
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.14
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.47
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.62
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.96
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.37
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  263.47
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.11
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.18
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7150.73
 p-value of test no 57                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 60                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.94
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 64                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.29
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.52
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  107.93
 p-value of test no 67                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.98
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46261
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870261
   j =  1                              :        399907481
   j =  2                              :            46255
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45814
 p-value of test no 71                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869814
   j =  1                              :        399908379
   j =  2                              :            45800
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 79                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 80                 :    0.81
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 81                 :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9900
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 95                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 105                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 106                :  3.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
 p-value of test no 107                :    0.9942
 
 Anderson-Darling statistic = A2       :    6.72
 p-value of test no 108                :  4.7e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 115                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.24
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.86
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.66
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.23
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.26
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.93
 p-value of test no 125                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.75
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-3
 p-value of test no 130                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.62
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.94
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17372.62
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.29
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.99
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.75
 p-value of test no 148                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.54
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.28
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.09
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.24
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.34
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.96
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.39
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.79
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.18
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  103.29
 p-value of test no 159                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.21
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.60
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.31
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.28
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.12
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.60
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.84
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.33
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4927.72
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.32
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.22
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.89
 p-value of test no 171                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.54
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.99
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.56
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.06
 p-value of test no 175                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.76
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.32
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.65
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.83
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.48
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.70
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.15
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9859.70
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.036
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.89
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.58
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4310.34
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.37
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11782.69
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12070.80
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.39
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000107227
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.53
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000010231
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 248                :    0.60
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 253                :    0.94
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:29.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  52  SampleProd, t = 24              4.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35766
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1476
 p-value of test no 5                  :  1.5e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334596
   j =  1                              :        599997048
   j =  2                              :             1476
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997313
   j =  2                              :             1342
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 9                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5516
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 26                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    2.81
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    2.48
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.79
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.14
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.65
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.30
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.72
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 52                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.28
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.89
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.61
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.20
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7118.45
 p-value of test no 57                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.61
 p-value of test no 58                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.06
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.38
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.79
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.55
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5091.25
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907538
   j =  2                              :            46228
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 73                 :    0.9903
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 76                 :  2.4e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
 p-value of test no 77                 :    0.9953
 
 Anderson-Darling statistic = A2       :    7.86
 p-value of test no 78                 :  1.4e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 87                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 108                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.08e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 117                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.53
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.94
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.65
 p-value of test no 121                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.47
 p-value of test no 122                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.77
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.00
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.82
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.57
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.88
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.38
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
 p-value of test no 143                :    0.9977
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17016.14
 p-value of test no 145                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.61
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.05
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.86
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.24
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.07
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.97
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.96
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.88
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.26
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.24
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.10
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.95
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.76
 p-value of test no 159                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.16
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.31
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.19
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.31
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.19
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  451.56
 p-value of test no 166                :  9.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.63
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.81
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.94
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.31
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.96
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.97
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.93
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.06
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.07
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.87
 p-value of test no 178                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.20
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 182                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 188                :    0.79
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.03
 p-value of test no 198                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.58
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.35
 p-value of test no 207                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 208                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9843.26
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 212                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 214                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10212.66
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.67
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4811.28
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.59
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.25
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12260.97
 p-value of test no 229                :  2.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11984.87
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.03
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000023956
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.56
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999963035
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 242                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.82
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.97
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:21.17
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35767
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 8                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 9                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 10                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5541
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7165
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4459
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    2.92
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.57
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.39
 p-value of test no 46                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.47
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.30
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.22
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.87
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.56
 p-value of test no 51                 :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.54
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.30
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.58
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  382.89
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1513.17
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.43
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.89
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.93
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.36
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.82
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9974
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46002
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870002
   j =  1                              :        399908001
   j =  2                              :            45992
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45726
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869726
   j =  1                              :        399908549
   j =  2                              :            45724
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 111                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.65e-6
 p-value of test no 113                :    0.9982
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.44
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.79
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.45
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.85
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.59
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.27
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.76
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.51
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.78
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.09
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.80
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.91
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 140                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.74
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17106.02
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.18
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.64
 p-value of test no 147                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.14
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.16
 p-value of test no 149                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.59
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.53
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.31
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.01
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.91
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.57
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.22
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.65
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.95
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.22
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.12
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.92
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.80
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.29
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  100.29
 p-value of test no 165                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.78
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.62
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.36
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.91
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.18
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.63
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.96
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.42
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.53
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.71
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.24
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 195                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.92
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.25
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.50
 p-value of test no 207                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10198.03
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 213                :    0.80
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9863.94
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.016
 p-value of test no 218                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.57
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 225                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.67
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.55
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4151.18
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.52
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11696.65
 p-value of test no 230                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999881213
 
 Normal statistic for number of bits   :   -0.94
 p-value of test no 232                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.80
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999906833
 
 Normal statistic for number of bits   :   -0.74
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 237                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.85
 p-value of test no 239                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.45
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.073
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:34.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35768
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4548
 p-value of test no 17                 :  7.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 21                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.02
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     934
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 29                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 44                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.13
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.54
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.33
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.22
 p-value of test no 50                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.43
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.32
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  199.46
 p-value of test no 54                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.78
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.89
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7225.74
 p-value of test no 57                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 59                 :    0.9914
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.53
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   44.44
 p-value of test no 65                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.96
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5022.77
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907977
   j =  2                              :            46007
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908680
   j =  2                              :            45657
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 101                :    0.90
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 108                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.31
 p-value of test no 118                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.54
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.43
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.20
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.55
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.26
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.52
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.43
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.32
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.74
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.76
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.75
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.62
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.00
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.53
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.01
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.93
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   17.05
 p-value of test no 152                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.69
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.33
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.86
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.94
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.41
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.86
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.30
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.05
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  190.25
 p-value of test no 161                :  8.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  198.93
 p-value of test no 162                :  2.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.47
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.03
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.88
 p-value of test no 165                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.32
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.07
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.91
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.46
 p-value of test no 169                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.56
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  327.02
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.47
 p-value of test no 172                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.14
 p-value of test no 173                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  397.62
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.53
 p-value of test no 175                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.40
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.67
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.05
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 195                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.57
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.35
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.78
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.57
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10072.87
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.83
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 219                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.63
 p-value of test no 222                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    3.03
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.45
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4136.82
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.59
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11970.44
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.56
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.85
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  7999872489
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.95
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000067372
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 250                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:09.20
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  17  BirthdaySpacings, t = 7         7.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35769
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 3                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 6                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7466
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 24                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     955
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    3.84
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 40                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 41                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.01
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.81
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.85
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.43
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.62
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.49
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.79
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  380.72
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.68
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.19
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.06
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.81
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.32
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.64
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46123
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870123
   j =  1                              :        399907757
   j =  2                              :            46117
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46032
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870032
   j =  1                              :        399907946
   j =  2                              :            46012
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 107                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 116                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.48
 p-value of test no 119                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.51
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.22
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.33
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.20
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.19
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.92
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.67
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.49
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.86
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.45
 p-value of test no 136                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.42
 p-value of test no 137                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.41
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17096.78
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.81
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.95
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.95
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.33
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.51
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.11
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.01
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.73
 p-value of test no 155                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.74
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.94
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.57
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.46
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.72
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.14
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.38
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.92
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.48
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.30
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.68
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.11
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.09
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.34
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.47
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.66
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.31
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.51
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.09
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 177                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.85
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.82
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 183                :    0.15
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 188                :    0.65
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
 p-value of test no 193                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.93
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 202                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.68
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.72
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.75
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.46
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.61
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.90
 p-value of test no 222                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.59
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4304.90
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4144.70
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.57
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11769.62
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.39
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  7999804758
 
 Normal statistic for number of bits   :   -1.54
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.16
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000137302
 
 Normal statistic for number of bits   :    1.09
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.78
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 243                :    0.73
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.66
 p-value of test no 249                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.61
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35770
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 8                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 11                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5479
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4491
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 20                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 33                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 34                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 35                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    3.09
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    4.34
 p-value of test no 45                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.03
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.96
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.04
 p-value of test no 48                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.02
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.01
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.39
 p-value of test no 51                 :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.62
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.73
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.38
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1319.37
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.37
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.02
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.50
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.10
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.85
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4997.00
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45431
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869431
   j =  1                              :        399909141
   j =  2                              :            45425
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908208
   j =  2                              :            45893
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 73                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 88                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 98                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 99                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 101                :    0.66
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.89
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.035
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.14
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.77
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.44
 p-value of test no 121                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.40
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.40
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.43
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.92
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.74
 p-value of test no 133                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.20
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.50
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 138                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.92
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17104.58
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.85
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.51
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.56
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.78
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.62
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.00
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.33
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.41
 p-value of test no 153                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.98
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.17
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.78
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.11
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.77
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.01
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   47.66
 p-value of test no 160                :    0.9926
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.48
 p-value of test no 161                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.10
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.84
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.33
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.04
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.62
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.40
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.82
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.87
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.01
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.34
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.74
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.97
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.46
 p-value of test no 174                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.50
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.68
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 177                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.36
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.016
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.29
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.67
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 200                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 202                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.79
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.97
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 209                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10192.33
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.10
 p-value of test no 215                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.18
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.79
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 225                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.27
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4031.68
 p-value of test no 227                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.75
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.95
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.56
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.09
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999843344
 
 Normal statistic for number of bits   :   -1.24
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.16
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000014674
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 243                :    0.74
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.38
 p-value of test no 254                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.56
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35771
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 15                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    3.44
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    3.49
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.73
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.48
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.49
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.11
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.60
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.49
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.46
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.78
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.81
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7090.59
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
 p-value of test no 58                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.63
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.55
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.07
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.25
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5176.17
 p-value of test no 68                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45516
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869516
   j =  1                              :        399908972
   j =  2                              :            45508
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908013
   j =  2                              :            45989
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 80                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 81                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 95                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 99                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 108                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.073
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.28
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.07
 p-value of test no 119                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.59
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.15
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.89
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.25
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.88
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 128                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.21
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.48
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   10.49
 p-value of test no 134                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 139                :    0.05
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.80
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17239.40
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.88
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.45
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.88
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.20
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.81
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.15
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.98
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.78
 p-value of test no 154                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.24
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.25
 p-value of test no 156                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.95
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.75
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.34
 p-value of test no 159                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  110.97
 p-value of test no 160                :  3.5e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.27
 p-value of test no 161                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.96
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  436.06
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.85
 p-value of test no 164                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.86
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.32
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.41
 p-value of test no 167                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.67
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.87
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.48
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.59
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.77
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.46
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.35
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.92
 p-value of test no 175                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.19
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.24
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    2.04
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 186                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.19
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.06
 p-value of test no 198                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.77
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
 p-value of test no 204                :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 205                :  6.1e-3
 
 Anderson-Darling statistic = A2       :    4.57
 p-value of test no 206                :  4.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  261.44
 p-value of test no 207                :  2.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10018.20
 p-value of test no 211                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10038.65
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 218                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 219                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5057.17
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.25
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.24
 p-value of test no 227                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.03
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12067.91
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.59
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.91
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999826709
 
 Normal statistic for number of bits   :   -1.37
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.80
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000102463
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 235                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 238                :    0.15
 
 Sample variance                       :    1.44
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 240                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 243                :    0.08
 
 Sample variance                       :    0.29
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 247                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:58.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35772
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4254
 p-value of test no 14                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 19                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 27                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.61
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.84
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.17
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.62
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.64
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.92
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.79
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.84
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.50
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.97
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.75
 p-value of test no 59                 :  9.9e-4    *****
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.93
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.96
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.96
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.26
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.46
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45993
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869993
   j =  1                              :        399908016
   j =  2                              :            45989
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45719
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869719
   j =  1                              :        399908564
   j =  2                              :            45715
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 72                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 77                 :    0.9913
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 78                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.8e-3
 
 Anderson-Darling statistic = A2       :    4.47
 p-value of test no 92                 :  5.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.54
 p-value of test no 115                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.80
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.80
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.50
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.59
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.10
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.37
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.52
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.26
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.84
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.73
 p-value of test no 133                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.28
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17543.92
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.07
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.65
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.94
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.66
 p-value of test no 149                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.84
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.68
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.81
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   43.55
 p-value of test no 154                :  8.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.73
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.39
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.79
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.38
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.27
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.35
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.39
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.38
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.39
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.13
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.48
 p-value of test no 167                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.72
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.45
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.53
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.92
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.26
 p-value of test no 172                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4877.47
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.11
 p-value of test no 174                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.78
 p-value of test no 175                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.57
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.16
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    0.41
 p-value of test no 184                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.73
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.08
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.79
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.75
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.44
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10070.87
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.21
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.22
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.99
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.55
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4046.66
 p-value of test no 227                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.76
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.61
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12073.90
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.80
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000032962
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.92
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999986540
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 237                :    0.9919
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
 p-value of test no 240                :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.43
 p-value of test no 243                :  7.5e-3
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35773
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 8                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 11                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 12                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5500
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7510
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    3.40
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.59
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    2.34
 p-value of test no 32                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.64
 p-value of test no 34                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    2.22
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 38                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.47
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.87
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.41
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.51
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.73
 p-value of test no 51                 :    0.9902
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.67
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  223.40
 p-value of test no 54                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.15
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.65
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6956.52
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.91
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.11
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.76
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.89
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.18
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46133
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870133
   j =  1                              :        399907737
   j =  2                              :            46127
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46152
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870152
   j =  1                              :        399907696
   j =  2                              :            46152
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 80                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-3
 p-value of test no 87                 :    0.9990
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.084
 p-value of test no 118                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.89
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.26
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.86
 p-value of test no 121                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.80
 p-value of test no 122                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.48
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.99
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.21
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.45
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.21
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.53
 p-value of test no 133                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.08
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.57
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 137                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.67
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17491.88
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.01
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.41
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.58
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.18
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.32
 p-value of test no 150                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.99
 p-value of test no 151                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.91
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.69
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.07
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.22
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.31
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.36
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.16
 p-value of test no 158                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.36
 p-value of test no 159                :    0.9904
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.88
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.28
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.38
 p-value of test no 162                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.12
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.95
 p-value of test no 164                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.23
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.88
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.35
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.37
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.59
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.09
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.15
 p-value of test no 171                :  9.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.56
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.18
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.49
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.11
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.82
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.77
 p-value of test no 177                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.52
 p-value of test no 178                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 181                :  5.9e-3
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.76
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 188                :    0.04
 
 Sample variance                       :    1.01
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.92
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.90
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.57
 p-value of test no 203                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.22
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.95
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9864.10
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 216                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5029.06
 p-value of test no 222                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.39
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4287.20
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.16
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.49
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.19
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.47
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999841400
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.23
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999885029
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 243                :    0.75
 
 Sample variance                       :    1.54
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 247                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.29
 p-value of test no 248                :    0.99
 
 Sample variance                       :    2.15
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 253                :    0.63
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:28.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35774
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5504
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     940
 p-value of test no 25                 :    0.09
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9975
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.32
 p-value of test no 28                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.60
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.44
 p-value of test no 48                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.27
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.71
 p-value of test no 50                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.45
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.26
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  271.84
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.36
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.81
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7041.07
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.64
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.30
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.08
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4984.33
 p-value of test no 68                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45649
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869649
   j =  1                              :        399908708
   j =  2                              :            45637
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908767
   j =  2                              :            45609
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 81                 :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 94                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.57e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.99
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.79
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.05
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.20
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.78
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.99
 p-value of test no 124                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.44
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.17
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.54
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.36
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.01
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.52
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.19
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.87
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.01
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.73
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.84
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.28
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.35
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.15
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.45
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.31
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.21
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.04
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.92
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.29
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.31
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.59
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.38
 p-value of test no 160                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.03
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.82
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.34
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.88
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.38
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.68
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.15
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4785.41
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  427.97
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.38
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.72
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.27
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.08
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.98
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.26
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.26
 p-value of test no 176                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.01
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.96
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.49
 p-value of test no 188                :    0.69
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.33
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.03
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 202                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.15
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.05
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.09
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.90
 p-value of test no 215                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 216                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.00
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 225                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.08
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.84
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.99
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.61
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.75
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999975242
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.21
 p-value of test no 233                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000126793
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 243                :    0.72
 
 Sample variance                       :    1.39
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 253                :    0.29
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35775
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4441
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    2.42
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    3.47
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.06
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.96
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.86
 p-value of test no 48                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.96
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.07
 p-value of test no 50                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.75
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.47
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.16
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.77
 p-value of test no 54                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  417.07
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1318.30
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7276.35
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.40
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.54
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.13
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.90
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45928
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869928
   j =  1                              :        399908146
   j =  2                              :            45924
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45661
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869661
   j =  1                              :        399908679
   j =  2                              :            45659
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 103                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
 p-value of test no 110                :    0.90
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.029
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.24
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.02
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.36
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.70
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.57
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.93
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.04
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.80
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.26
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.69
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.84
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.53
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.61
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.95
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.38
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.71
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.01
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.43
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.96
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.92
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.70
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.25
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.36
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.77
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.36
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.68
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.30
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.19
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.28
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.53
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.22
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.26
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.10
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.24
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  449.81
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.13
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.47
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.00
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.70
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.41
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9929
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.93
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.06
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
 p-value of test no 201                :    0.9970
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.30
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.26
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10019.40
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.95
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4807.24
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
 p-value of test no 223                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 224                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5024.20
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4284.79
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.94
 p-value of test no 228                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.91
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11656.06
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.31
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999911855
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.94
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000031006
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.29
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 240                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.13
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.68
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.40
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.023
 p-value of test no 253                :    0.51
 
 Sample variance                       :    0.93
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:34.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35776
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 8                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 20                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7164
 p-value of test no 21                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    3.74
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 42                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.43
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.84
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.33
 p-value of test no 48                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.25
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.80
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.44
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.60
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.06
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1531.10
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.47
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.07
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.81
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.30
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.13
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908622
   j =  2                              :            45680
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46124
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870124
   j =  1                              :        399907756
   j =  2                              :            46116
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 95                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 99                 :    0.9997    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
 p-value of test no 109                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 118                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.83
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.94
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.70
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.51
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.25
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 128                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.84
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.07
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.62
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.20
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17616.03
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.80
 p-value of test no 146                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.43
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.62
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.02
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.71
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.16
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.93
 p-value of test no 152                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.42
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.91
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.24
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.02
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.76
 p-value of test no 157                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.28
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.33
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.54
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.93
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.13
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.70
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.44
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.51
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.77
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.73
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5062.84
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.27
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.95
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.23
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.43
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.50
 p-value of test no 174                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.51
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.24
 p-value of test no 178                :    0.9936
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 183                :    0.24
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
 p-value of test no 190                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.93
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 197                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.78
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.11
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.51
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10140.72
 p-value of test no 211                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.73
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.29
 p-value of test no 222                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    5.10
 p-value of test no 225                :  2.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5169.31
 p-value of test no 226                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4010.22
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.96
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.97
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.14
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.08
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000127294
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.06
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999949580
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.070
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.56
 p-value of test no 239                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 243                :    0.29
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:54.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft AD, t = 32               0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35777
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 3                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 4                  :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 14                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 21                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.95
 p-value of test no 34                 :  3.8e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.37
 p-value of test no 47                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.75
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.58
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.71
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.26
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.79
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.56
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.16
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.72
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7045.96
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
 p-value of test no 58                 :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   48.20
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.06
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.57
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.21
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908360
   j =  2                              :            45817
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45917
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869917
   j =  1                              :        399908168
   j =  2                              :            45913
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 78                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 98                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 102                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.27
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.19
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.40
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.23
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.81
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.80
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   44.50
 p-value of test no 125                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 127                :    0.99
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.63
 p-value of test no 129                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.01
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.20
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.90
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.66
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17252.90
 p-value of test no 145                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.41
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.81
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.82
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.76
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.67
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.54
 p-value of test no 151                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.90
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.36
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.91
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.20
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.96
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.35
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.45
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.93
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.92
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.55
 p-value of test no 163                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.49
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.52
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.63
 p-value of test no 166                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.84
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.85
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  307.03
 p-value of test no 169                :    0.9969
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  224.98
 p-value of test no 170                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.63
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.20
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4952.11
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.08
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  265.05
 p-value of test no 175                :  1.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.29
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.20
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.55
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.69
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.85
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.46
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 204                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    4.15
 p-value of test no 206                :  7.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  151.09
 p-value of test no 207                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10245.71
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10108.19
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.73
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4753.05
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.88
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4000.94
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11853.02
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.12
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.76
 p-value of test no 231                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000001105
 
 Normal statistic for number of bits   : 8.74e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000043546
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 237                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.048
 p-value of test no 243                :    0.52
 
 Sample variance                       :    1.51
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.18
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.39
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.78
 p-value of test no 254                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:04.11
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            3.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35778
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 9                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 10                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5520
 p-value of test no 13                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 14                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 15                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.45
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.38
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    5.17
 p-value of test no 36                 :  2.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     346
 p-value of test no 37                 :  5.0e-3
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.90
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.64
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.11
 p-value of test no 50                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.74
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.10
 p-value of test no 52                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.39
 p-value of test no 53                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.19
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  432.72
 p-value of test no 55                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.92
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7037.22
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.35
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.13
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.95
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.80
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5099.55
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45669
 p-value of test no 70                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869669
   j =  1                              :        399908664
   j =  2                              :            45665
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46356
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870356
   j =  1                              :        399907297
   j =  2                              :            46338
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 74                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 106                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 110                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.86
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.051
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.25
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.04
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.17
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.64
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.39
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.76
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.56
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.19
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 134                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.83
 p-value of test no 135                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.61
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17424.22
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   63.80
 p-value of test no 146                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.46
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.58
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.27
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.51
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.33
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.39
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.42
 p-value of test no 154                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.26
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.53
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.82
 p-value of test no 157                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  454.87
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.32
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.40
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.14
 p-value of test no 161                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.22
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  429.16
 p-value of test no 163                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.23
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.62
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.02
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.09
 p-value of test no 167                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.01
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.08
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.39
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.41
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.80
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.12
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.18
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.88
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.79
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.67
 p-value of test no 177                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.61
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.63
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 188                :    0.80
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.83
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.26
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.12
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.40
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 208                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.22
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.41
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4973.65
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 225                :    0.9958
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.39
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.98
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4299.62
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.90
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.83
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.42
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000174040
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.34
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999937673
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.09
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 247                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 248                :    0.92
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.076
 p-value of test no 253                :    0.53
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:19.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35779
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 8                  :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 22                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 26                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.87
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     620
 p-value of test no 31                 :    0.21
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 33                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.23
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.80
 p-value of test no 35                 :  3.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.82
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.31
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.00
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.40
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.00
 p-value of test no 51                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.61
 p-value of test no 52                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.82
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  253.04
 p-value of test no 54                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  367.67
 p-value of test no 55                 :    0.9907
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1468.65
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.94
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.93
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.37
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.21
 p-value of test no 66                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.84
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4905.60
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908028
   j =  2                              :            45980
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45979
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869979
   j =  1                              :        399908046
   j =  2                              :            45971
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 73                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 108                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
 p-value of test no 110                :    0.13
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.034
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.27
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.01
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.73
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.30
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.99
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.13
 p-value of test no 125                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.26
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 131                :    0.94
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 132                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.88
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.35
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    3.14
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.52
 p-value of test no 141                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17422.20
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.40
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.36
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.50
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.15
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.12
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.28
 p-value of test no 151                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.78
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.46
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.49
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.36
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.53
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.11
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.72
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.53
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.26
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.56
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.57
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.45
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.78
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.14
 p-value of test no 166                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.52
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.14
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.36
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.90
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.56
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.85
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.86
 p-value of test no 174                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.32
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.17
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.20
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.04
 p-value of test no 184                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 188                :    0.94
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.81
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
 p-value of test no 200                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.17
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.19
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9906.81
 p-value of test no 211                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.03
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.81
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.80
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.50
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.53
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.62
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.90
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.24
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000094843
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.01
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000055438
 
 Normal statistic for number of bits   :    0.44
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    1.30
 p-value of test no 239                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.13
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 245                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.15
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:49.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35780
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 9                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5476
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 17                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 18                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 19                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7454
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     839
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 27                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 32                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 34                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.51
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.56
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.04
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.47
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.52
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.65
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.00
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.88
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.86
 p-value of test no 54                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.93
 p-value of test no 55                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1571.62
 p-value of test no 56                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.89
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.36
 p-value of test no 61                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   88.46
 p-value of test no 65                 :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.58
 p-value of test no 66                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.87
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4850.71
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908329
   j =  2                              :            45834
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 71                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908543
   j =  2                              :            45724
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 76                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.88
 p-value of test no 119                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.09
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.23
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.44
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.37
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.42
 p-value of test no 125                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.46
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.80
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.74
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.85
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.24
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17155.93
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.96
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.89
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.49
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.41
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.97
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.91
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.29
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.49
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.69
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.83
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.80
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.49
 p-value of test no 159                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.29
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  201.31
 p-value of test no 161                :  1.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.27
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  570.17
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.59
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.37
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.35
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.05
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4817.36
 p-value of test no 168                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.07
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.90
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  457.87
 p-value of test no 171                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.49
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.67
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.69
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.49
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.19
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.87
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.05
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.083
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-3
 p-value of test no 191                :    0.96
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.57
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.47
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.30
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.66
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9737.88
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.99
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.94
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.81
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.51
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4143.68
 p-value of test no 228                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.23
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.21
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.06
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999876353
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.33
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999890939
 
 Normal statistic for number of bits   :   -0.86
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.91
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.040
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.11
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:22.67
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35781
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 11                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5536
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 15                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 16                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7185
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.44
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 29                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    3.16
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.68
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.32
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.08
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.82
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.79
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.21
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.70
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.68
 p-value of test no 53                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.54
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  402.56
 p-value of test no 55                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.21
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7091.39
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.45
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.79
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.16
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.92
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5114.66
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46158
 p-value of test no 70                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870158
   j =  1                              :        399907685
   j =  2                              :            46156
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45787
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869787
   j =  1                              :        399908429
   j =  2                              :            45781
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 72                 :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 93                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.57
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 109                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.34e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.84
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.66
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.57
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.92
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.90
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.21
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.87
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.12
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.70
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.32
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.45
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.03
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.63
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 142                :    0.9929
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.07
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17851.82
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.80
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.92
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.91
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.89
 p-value of test no 149                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.32
 p-value of test no 150                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.37
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.98
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.64
 p-value of test no 154                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.70
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.87
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.20
 p-value of test no 158                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.12
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.98
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.17
 p-value of test no 161                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.35
 p-value of test no 162                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.59
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.92
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.68
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  427.12
 p-value of test no 166                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.82
 p-value of test no 167                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5018.10
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.56
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.14
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.75
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.92
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.31
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.65
 p-value of test no 174                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.47
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.42
 p-value of test no 176                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.94
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 186                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 188                :    0.78
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.75
 p-value of test no 196                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.75
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.31
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.76
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.73
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.39
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.74
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.71
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.62
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4195.54
 p-value of test no 227                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.79
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12091.94
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.74
 p-value of test no 230                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.69
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000024481
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.02
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000041458
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.072
 p-value of test no 238                :    0.47
 
 Sample variance                       :    0.98
 p-value of test no 239                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.27
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 248                :    0.23
 
 Sample variance                       :    0.37
 p-value of test no 249                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.039
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:25.30
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35782
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5512
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4263
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4202
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     874
 p-value of test no 25                 :    0.80
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 28                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.94
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 33                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 39                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.56
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.57
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 48                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.72
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.31
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.69
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.11
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.80
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.54
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.49
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1515.12
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.40
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.00
 p-value of test no 61                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.86
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.13
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.75
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5055.59
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908501
   j =  2                              :            45745
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45874
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869874
   j =  1                              :        399908255
   j =  2                              :            45868
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 99                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 102                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 105                :    0.9966
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.73
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.92
 p-value of test no 121                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.35
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.73
 p-value of test no 123                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.03
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.74
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.54
 p-value of test no 129                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.02
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.23
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.46
 p-value of test no 141                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17689.45
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.69
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.28
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.78
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.83
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.45
 p-value of test no 150                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.40
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.50
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.26
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.83
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.58
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.90
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.31
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.17
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.06
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.57
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.69
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.21
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.26
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.71
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.19
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.34
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.71
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.68
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.38
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.32
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.99
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.97
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.07
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.37
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.07
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.43
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 178                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.75
 p-value of test no 179                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.60
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
 p-value of test no 191                :    0.90
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 192                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
 p-value of test no 193                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.70
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.05
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.42
 p-value of test no 203                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.34
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.59
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9777.95
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 218                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.54
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4942.13
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.07
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.01
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.58
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.86
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.55
 p-value of test no 231                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999867815
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.90
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  7999882602
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 235                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.15
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 248                :    0.78
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.17
 p-value of test no 253                :    0.02
 
 Sample variance                       :    0.56
 p-value of test no 254                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:01.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35783
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 3                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 8                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 9                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 15                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 30                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     652
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.26
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.96
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.37
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.38
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.02
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.35
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.49
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.94
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  436.16
 p-value of test no 55                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.42
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7131.41
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.29
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.52
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.64
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.88
 p-value of test no 67                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5127.71
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45541
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869541
   j =  1                              :        399908923
   j =  2                              :            45531
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908081
   j =  2                              :            45955
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  9.7e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.12
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 108                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
 p-value of test no 112                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 118                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.20
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.99
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.25
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.99
 p-value of test no 122                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.34
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.15
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.98
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.20
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 132                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.41
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.62
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.94
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.21
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.62
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.32
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.71
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.52
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.21
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.84
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.48
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.63
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.04
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.66
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.76
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.14
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.72
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.74
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.09
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.83
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.48
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.36
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.04
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.15
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.19
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  431.97
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.88
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.42
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.29
 p-value of test no 170                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.03
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.06
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5019.07
 p-value of test no 173                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.99
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.31
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.78
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.77
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.35
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.55
 p-value of test no 179                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.75
 p-value of test no 198                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.18
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 206                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.03
 p-value of test no 207                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.45
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9992.96
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.94
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 223                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 225                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.84
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.73
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.08
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11496.50
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11583.18
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.85
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999948944
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.03
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999944759
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 240                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 252                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.57
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:58.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35784
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 14                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7443
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7566
 p-value of test no 18                 :  2.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 21                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     889
 p-value of test no 25                 :    0.63
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9945
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.87
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.13
 p-value of test no 30                 :    0.9995    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 32                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.31
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.66
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.65
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.23
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.59
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.62
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.93
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.90
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.89
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.17
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.75
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6990.74
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.95
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.54
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.89
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.78
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4919.76
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46211
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870211
   j =  1                              :        399907585
   j =  2                              :            46197
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45560
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869560
   j =  1                              :        399908884
   j =  2                              :            45552
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 76                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    4.74
 p-value of test no 78                 :  3.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
 p-value of test no 84                 :    0.9915
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 102                :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 106                :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    3.46
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 111                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.18
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 117                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.73
 p-value of test no 118                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.24
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.66
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.69
 p-value of test no 121                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.10
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.71
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.96
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 128                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.50
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.55
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.29
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.27
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 135                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.53
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.98
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17821.50
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.08
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.53
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.13
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.98
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.38
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.09
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.77
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.27
 p-value of test no 153                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.58
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.52
 p-value of test no 155                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.54
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.84
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.69
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.07
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.94
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.55
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.41
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  541.39
 p-value of test no 163                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.28
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.93
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.64
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.14
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.39
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  424.48
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.62
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.22
 p-value of test no 171                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.27
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.24
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.45
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.55
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.79
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.79
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 186                :    0.03
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 188                :    0.08
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.77
 p-value of test no 198                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.63
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.91
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10105.64
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.67
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.97
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4943.00
 p-value of test no 226                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.40
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4064.27
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11579.51
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.29
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.54
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000208939
 
 Normal statistic for number of bits   :    1.65
 p-value of test no 232                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.25
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000141304
 
 Normal statistic for number of bits   :    1.12
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 238                :    0.02
 
 Sample variance                       :    1.04
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 247                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 250                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 253                :    0.91
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:51.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP1, t = 5          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35785
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 8                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1486
 p-value of test no 9                  :  6.0e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334606
   j =  1                              :        599997028
   j =  2                              :             1486
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7121
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 18                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7099
 p-value of test no 21                 :    0.9949
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    3.06
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.28
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     128
 p-value of test no 43                 :    0.96
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.19
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.70
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.39
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.98
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.95
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.51
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.76
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.13
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.38
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.42
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.35
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.98
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.72
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.83
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.37
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5097.12
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46063
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870063
   j =  1                              :        399907883
   j =  2                              :            46045
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45983
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869983
   j =  1                              :        399908038
   j =  2                              :            45975
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 78                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 84                 :  2.4e-4    *****
 
 Anderson-Darling statistic = A2       :    4.86
 p-value of test no 85                 :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 103                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 111                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.29
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.90
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.23
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.28
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.34
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.18
 p-value of test no 124                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.57
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.20
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.20
 p-value of test no 133                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.44
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 135                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.01
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 143                :    0.78
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17373.76
 p-value of test no 145                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.35
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.58
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.31
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.35
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.32
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.68
 p-value of test no 153                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.77
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.59
 p-value of test no 155                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.65
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.20
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  425.05
 p-value of test no 158                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.50
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  114.46
 p-value of test no 160                :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.23
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.72
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.91
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.05
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.47
 p-value of test no 165                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  478.88
 p-value of test no 166                :  6.9e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.74
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.24
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.66
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.67
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.35
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.23
 p-value of test no 172                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.75
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.10
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.43
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.64
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.72
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.00
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.41
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 185                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.25
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.33
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.54
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.50
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.03
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9745.49
 p-value of test no 215                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 221                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.41
 p-value of test no 222                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4669.01
 p-value of test no 226                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.53
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4172.54
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.56
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11566.09
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.65
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000087808
 
 Normal statistic for number of bits   :    0.69
 p-value of test no 232                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.17
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000070060
 
 Normal statistic for number of bits   :    0.55
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 243                :    0.06
 
 Sample variance                       :    0.77
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 248                :    0.70
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:35.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           6.0e-4
  78  RandomWalk1 H (L=10000, r=0)    6.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35786
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5270
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7486
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 19                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 21                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.69
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    2.37
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.40
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.55
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.82
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.41
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.47
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.59
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.11
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.41
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.87
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7136.72
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.79
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.49
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.88
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.27
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5240.08
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45611
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869611
   j =  1                              :        399908783
   j =  2                              :            45601
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45720
 p-value of test no 71                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869720
   j =  1                              :        399908563
   j =  2                              :            45714
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
 p-value of test no 76                 :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 92                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.25e-5
 p-value of test no 109                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-5
 p-value of test no 112                :    0.9906
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.70
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.61
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.10
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.09
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.53
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.18
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.62
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.29
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.11
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.34
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.95
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 136                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.49
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 144                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17639.60
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.60
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.87
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.35
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.86
 p-value of test no 149                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.16
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.93
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.09
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.22
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.74
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.70
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.56
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.87
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.86
 p-value of test no 158                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.49
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.63
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.08
 p-value of test no 161                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.96
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.51
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.55
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.50
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.39
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.81
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.12
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.68
 p-value of test no 169                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.37
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.97
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.48
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.54
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.19
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.84
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.58
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 178                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.76
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 187                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 188                :    0.12
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.81
 p-value of test no 196                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.69
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  234.53
 p-value of test no 207                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9875.87
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 214                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9711.51
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.49
 p-value of test no 216                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.03
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.33
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.60
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.66
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.28
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11675.23
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.25
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000070342
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   86.21
 p-value of test no 233                :  3.5e-3
 
 
 -----------------------------------------------
 Total number of bits:  8000053992
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 238                :    0.95
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.44
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:35.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35787
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 10                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5396
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 20                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 21                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.00
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.80
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.33
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.09
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.05
 p-value of test no 40                 :  9.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.88
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.99
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.60
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.01
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.33
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.66
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.28
 p-value of test no 51                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.38
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.96
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  205.36
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.09
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.01
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6882.02
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.59
 p-value of test no 58                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 59                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 60                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   13.73
 p-value of test no 61                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.77
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.32
 p-value of test no 66                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.03
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4955.80
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908212
   j =  2                              :            45885
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908280
   j =  2                              :            45857
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 74                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 83                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 92                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 104                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 116                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.48
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.46
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.45
 p-value of test no 121                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.30
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.67
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.74
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.72
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 131                :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.50
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.82
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.61
 p-value of test no 141                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17588.26
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.92
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.23
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.86
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.89
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.38
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.07
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.42
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.37
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.33
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.50
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.84
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.54
 p-value of test no 158                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.43
 p-value of test no 159                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.40
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.45
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.43
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.63
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.69
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.68
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.72
 p-value of test no 166                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.69
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.86
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.40
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.82
 p-value of test no 170                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.28
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.20
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.02
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.51
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.17
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.36
 p-value of test no 176                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.81
 p-value of test no 178                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 186                :    0.9999    *****
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.33
 p-value of test no 188                :    0.99
 
 Sample variance                       :    1.74
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.92
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.61
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.85
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.62
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.51
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.90
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 221                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.48
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4859.23
 p-value of test no 226                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.30
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.04
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.43
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12048.59
 p-value of test no 230                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.10
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  7999894479
 
 Normal statistic for number of bits   :   -0.83
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.31
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000010204
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 234                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.47
 p-value of test no 238                :    0.93
 
 Sample variance                       :    1.45
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 248                :    0.85
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    1.71
 p-value of test no 254                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:52.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35788
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 9                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4295
 p-value of test no 16                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.54
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     583
 p-value of test no 31                 :    0.75
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.63
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.12
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.01
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.33
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.64
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.10
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.31
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.22
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1540.92
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7043.79
 p-value of test no 57                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.81
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.52
 p-value of test no 65                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.49
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.76
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4961.08
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45510
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869510
   j =  1                              :        399908981
   j =  2                              :            45508
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45869
 p-value of test no 71                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869869
   j =  1                              :        399908265
   j =  2                              :            45863
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.02
 p-value of test no 88                 :  8.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 108                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 118                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.63
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.90
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.40
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.65
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.92
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.77
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.51
 p-value of test no 129                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.68
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.30
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.47
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17672.84
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.53
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.36
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.69
 p-value of test no 148                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.80
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.30
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.95
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.09
 p-value of test no 152                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.95
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.28
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.36
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.31
 p-value of test no 156                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.84
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.56
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.07
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.12
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.22
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.84
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.71
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.96
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.82
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  452.23
 p-value of test no 166                :  9.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.23
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4977.79
 p-value of test no 168                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.01
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.39
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.81
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.67
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.86
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.67
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.30
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.68
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.04
 p-value of test no 178                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.30
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9942
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.67
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 192                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.56
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.37
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.04
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.67
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.07
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.35
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 217                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.61
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.79
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.17
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.84
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.18
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11781.23
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.45
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999932231
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.85
 p-value of test no 233                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  7999911600
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 235                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 241                :    0.89
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 242                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.51
 p-value of test no 243                :    0.93
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 248                :    0.16
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 251                :    0.85
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.34
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:17.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35789
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5558
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 16                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 20                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.99
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    2.31
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.17
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.87
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.39
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.76
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.11
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.19
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.73
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.18
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.48
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.68
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1539.16
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6941.01
 p-value of test no 57                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.75
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.21
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.10
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.93
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5166.26
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908485
   j =  2                              :            45744
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46445
 p-value of test no 71                 :  4.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870445
   j =  1                              :        399907116
   j =  2                              :            46433
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
 p-value of test no 101                :    0.99
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 113                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.05
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.69
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.55
 p-value of test no 122                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.01
 p-value of test no 123                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.45
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.97
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.49
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.03
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.06
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.39
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17084.02
 p-value of test no 145                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.26
 p-value of test no 146                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.05
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.12
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.48
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.04
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.49
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.28
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.88
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.17
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.89
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.91
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.93
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.62
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  112.37
 p-value of test no 159                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.18
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.50
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.44
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.47
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.96
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.56
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.02
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.38
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5124.34
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.70
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.70
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.97
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.78
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.93
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.88
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.68
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.19
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.28
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.39
 p-value of test no 184                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 187                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.97
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.89
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.04
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 200                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.27
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.45
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9870.18
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.71
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 218                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4835.68
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4830.74
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4257.95
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4148.35
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12171.49
 p-value of test no 229                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12249.05
 p-value of test no 230                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.14
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000043543
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.01
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000024679
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 235                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 242                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:05.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35790
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 7                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 9                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5281
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 17                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7100
 p-value of test no 20                 :    0.9947
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 21                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 28                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    3.56
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     553
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 33                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 40                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 45                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.47
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.57
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.83
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.85
 p-value of test no 50                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.48
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.30
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.72
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.49
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.60
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.84
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 59                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.71
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 62                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.77
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.27
 p-value of test no 66                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.00
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.21
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45756
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869756
   j =  1                              :        399908493
   j =  2                              :            45746
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45664
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869664
   j =  1                              :        399908674
   j =  2                              :            45660
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 78                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 87                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 116                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.16
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.10
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.42
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.47
 p-value of test no 124                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.38
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 126                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.59
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.95
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.90
 p-value of test no 134                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.12
 p-value of test no 141                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17509.93
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.35
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.09
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.50
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.20
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.49
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.82
 p-value of test no 152                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.34
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.42
 p-value of test no 154                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.56
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.02
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.86
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.41
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.37
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.73
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.11
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.31
 p-value of test no 162                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.74
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.75
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.35
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.55
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.41
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5123.71
 p-value of test no 168                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.34
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.69
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.11
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.13
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.14
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.98
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.74
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.10
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.81
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.43
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 195                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.98
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.84
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.72
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.22
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.64
 p-value of test no 207                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.01
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.58
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.51
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5011.49
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.55
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4266.98
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.93
 p-value of test no 228                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.25
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.58
 p-value of test no 230                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.11
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000120859
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.36
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  7999927623
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 243                :    0.26
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35791
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 7                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 9                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997435
   j =  2                              :             1281
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 10                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 22                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.70
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.97
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    4.16
 p-value of test no 33                 :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.89
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.46
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.49
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.29
 p-value of test no 49                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.14
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 53                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.26
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.04
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.93
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6992.28
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.04
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.65
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.77
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.90
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.09
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907629
   j =  2                              :            46175
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908531
   j =  2                              :            45733
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 83                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 108                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.70e-4
 p-value of test no 109                :  4.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    3.91
 p-value of test no 111                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 116                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.42
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.34
 p-value of test no 120                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.51
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.94
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.45
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.92
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.98
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.97
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 133                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.02
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.88
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.54
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17213.29
 p-value of test no 145                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.34
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.29
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.69
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.64
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.92
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.43
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.56
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.22
 p-value of test no 154                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.92
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.28
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.01
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.37
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.09
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.93
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.82
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.84
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.59
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.64
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.89
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.73
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.42
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.33
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.87
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.21
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.25
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.41
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.37
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.29
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.18
 p-value of test no 176                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.53
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.00
 p-value of test no 179                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.75
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 190                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.22
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.78
 p-value of test no 198                :    0.46
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.71
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.35
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.21
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.17
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 221                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.61
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4823.20
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3992.39
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4231.28
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11440.20
 p-value of test no 229                :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12107.21
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.96
 p-value of test no 231                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000115048
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.12
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999911456
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.54
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:54.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35792
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  9.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997379
   j =  2                              :             1309
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 7                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 11                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5329
 p-value of test no 13                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 17                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7275
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.67
 p-value of test no 22                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.37
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 24                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 35                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.27
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.23
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.36
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.37
 p-value of test no 49                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.67
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.16
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.73
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.24
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.25
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  381.79
 p-value of test no 55                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.72
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.07
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.89
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.83
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.91
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.34
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907946
   j =  2                              :            46021
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 71                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907941
   j =  2                              :            46028
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 81                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 92                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 94                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 99                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.08e-4
 p-value of test no 109                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    4.22
 p-value of test no 111                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.079
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.65
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.23
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.81
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.11
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.63
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.12
 p-value of test no 124                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.65
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.83
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.55
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.32
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.58
 p-value of test no 137                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 139                :    0.85
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.16
 p-value of test no 141                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 144                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17434.33
 p-value of test no 145                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.43
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.56
 p-value of test no 149                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.98
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.63
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.92
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.96
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.12
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.33
 p-value of test no 155                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.38
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.88
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.53
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.81
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.82
 p-value of test no 161                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.64
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  554.75
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.74
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.76
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.12
 p-value of test no 166                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.85
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4943.79
 p-value of test no 168                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.20
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.86
 p-value of test no 170                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.01
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.55
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4857.57
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.64
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.22
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.12
 p-value of test no 176                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.00
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.53
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.26
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.55
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 204                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.30
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.52
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.44
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.52
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.03
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 218                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 220                :    0.90
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.68
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 223                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5118.88
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.00
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4230.74
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.67
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.43
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.77
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  7999990137
 
 Normal statistic for number of bits   :  -0.078
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.29
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999964625
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 241                :    0.94
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 242                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.57
 p-value of test no 243                :    0.94
 
 Sample variance                       :    1.24
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.28
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 253                :    0.72
 
 Sample variance                       :    1.51
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:52.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35793
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 3                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 10                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 14                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 19                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    4.29
 p-value of test no 26                 :  6.3e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 27                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 28                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.43
 p-value of test no 33                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.20
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.57
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.63
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 49                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.86
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.48
 p-value of test no 51                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.46
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.58
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.82
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1512.92
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7230.39
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.94
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.19
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.63
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.82
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5129.11
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908461
   j =  2                              :            45765
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45523
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908959
   j =  2                              :            45513
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 76                 :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 87                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 88                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 91                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 92                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 101                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.88
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.60
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.52
 p-value of test no 121                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.94
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.23
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.22
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.37
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.26
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.41
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.72
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.26
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.91
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.15
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.76
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.01
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.91
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.15
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.72
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.65
 p-value of test no 151                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.09
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.79
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.55
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.60
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.17
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.79
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.95
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.66
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.51
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.15
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.57
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.59
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.39
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.51
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  473.35
 p-value of test no 167                :  1.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5148.73
 p-value of test no 168                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.15
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.18
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.54
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.01
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.38
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.95
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.59
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.25
 p-value of test no 177                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.56
 p-value of test no 178                :    0.9901
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.32
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
 p-value of test no 191                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 195                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.84
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.25
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.91
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9852.28
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9940.42
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.39
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 218                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.17
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.17
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.70
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.08
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.62
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4018.86
 p-value of test no 228                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12125.06
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.42
 p-value of test no 230                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.59
 p-value of test no 231                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000104767
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.31
 p-value of test no 233                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  8000149554
 
 Normal statistic for number of bits   :    1.18
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 235                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 238                :    0.17
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    1.33
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 247                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 248                :    0.71
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35794
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 3                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5322
 p-value of test no 13                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 17                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 35                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 36                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 42                 :    0.9942
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.01
 p-value of test no 46                 :    0.9946
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.92
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.65
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.17
 p-value of test no 50                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.19
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.48
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.88
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.99
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.79
 p-value of test no 55                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1373.88
 p-value of test no 56                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6905.49
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.54
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.99
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.64
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.80
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907885
   j =  2                              :            46047
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46146
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870146
   j =  1                              :        399907712
   j =  2                              :            46138
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 74                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 80                 :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.12
 p-value of test no 81                 :  7.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  9.4e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 85                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 86                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 93                 :  5.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    2.95
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 98                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 103                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 111                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.91
 p-value of test no 117                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.03
 p-value of test no 119                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.25
 p-value of test no 120                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.34
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   67.11
 p-value of test no 122                :  1.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.63
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.01
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.32
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.05
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.70
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.00
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.66
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 142                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17097.12
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.25
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.37
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.29
 p-value of test no 148                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.04
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.31
 p-value of test no 150                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.80
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.24
 p-value of test no 152                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.15
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.06
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.60
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.63
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.03
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.47
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.50
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.70
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.63
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.82
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.10
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.95
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.70
 p-value of test no 166                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.84
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.27
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.57
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.26
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.84
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.19
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4944.88
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.61
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.91
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.21
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.69
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.44
 
 Sample variance                       :    0.14
 p-value of test no 184                :    0.9987
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 195                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.14
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.12
 p-value of test no 198                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.18
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.55
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 210                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10206.95
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 213                :    0.76
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9926.23
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.51
 p-value of test no 216                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.028
 p-value of test no 217                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4957.51
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.36
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4190.05
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.23
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.87
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11994.00
 p-value of test no 230                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.27
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000045727
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.89
 p-value of test no 233                :    0.52
 
 
 -----------------------------------------------
 Total number of bits:  8000081961
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.67
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 247                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.014
 p-value of test no 248                :    0.49
 
 Sample variance                       :    0.98
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 251                :  5.3e-3
 
 Anderson-Darling statistic = A2       :    3.61
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.47
 p-value of test no 253                :  6.8e-3
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:17.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35795
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1264
 p-value of test no 9                  :    0.9968
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334384
   j =  1                              :        599997472
   j =  2                              :             1264
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4250
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7135
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7415
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     937
 p-value of test no 25                 :    0.11
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 32                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 39                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 44                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 45                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.62
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.64
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.11
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.19
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.88
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.51
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.59
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.64
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.40
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.54
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.55
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 64                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.69
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.97
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.38
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5023.71
 p-value of test no 68                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908386
   j =  2                              :            45798
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908302
   j =  2                              :            45843
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 87                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 103                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 114                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 117                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.55
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.15
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.48
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.34
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.04
 p-value of test no 124                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.18
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
 p-value of test no 126                :    0.9935
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.85
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 130                :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.89
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.04
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.47
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.07
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17303.52
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.63
 p-value of test no 146                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.53
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.22
 p-value of test no 148                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.27
 p-value of test no 149                :    0.9934
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.42
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.85
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.65
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   44.95
 p-value of test no 153                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.39
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.46
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.64
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.28
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.36
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.65
 p-value of test no 160                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.97
 p-value of test no 162                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.25
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.08
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.05
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.09
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.25
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4898.68
 p-value of test no 168                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.92
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.64
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.08
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.90
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.97
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.79
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.68
 p-value of test no 175                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.39
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.03
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.26
 p-value of test no 179                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.02
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.51
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.35
 p-value of test no 207                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.45
 p-value of test no 211                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
 p-value of test no 213                :    0.9933
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9730.25
 p-value of test no 215                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 218                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4796.98
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.18
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4017.82
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4179.92
 p-value of test no 228                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11983.73
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.88
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.54
 p-value of test no 231                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000035677
 
 Normal statistic for number of bits   :    0.28
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.04
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000021082
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 243                :    0.60
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.046
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 253                :    0.73
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:55.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35796
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 4                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 8                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5539
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 14                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 16                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4439
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 19                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    2.38
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.65
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.08
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 41                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    2.78
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.21
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.51
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.63
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.02
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.01
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.52
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  384.80
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.02
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.93
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
 p-value of test no 59                 :    0.9959
 
 Anderson-Darling statistic = A2       :    3.13
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.31
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.49
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.47
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.05
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46192
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870192
   j =  1                              :        399907619
   j =  2                              :            46186
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46039
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870039
   j =  1                              :        399907925
   j =  2                              :            46033
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 92                 :    0.9931
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.58e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 117                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.51
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.62
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.33
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.37
 p-value of test no 122                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.95
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.81
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.49
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.26
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.84
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.27
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.87
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.42
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.49
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 144                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17190.82
 p-value of test no 145                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.98
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.59
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.00
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.54
 p-value of test no 149                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.45
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   59.42
 p-value of test no 151                :  8.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.95
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.74
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.27
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.74
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.52
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.77
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.70
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.03
 p-value of test no 161                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.41
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.73
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.22
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.04
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.15
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.01
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.02
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.12
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.52
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.64
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.39
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.50
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.18
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.92
 p-value of test no 175                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.93
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.12
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.89
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.63
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.27
 p-value of test no 184                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.48
 p-value of test no 189                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.20
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.30
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9832.46
 p-value of test no 211                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.48
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.39
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 221                :    0.9917
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.08
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.18
 p-value of test no 226                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4270.52
 p-value of test no 227                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3949.20
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.01
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11499.17
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.66
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000010198
 
 Normal statistic for number of bits   :   0.081
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.13
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000148570
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 242                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 248                :    0.30
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 253                :    0.37
 
 Sample variance                       :    0.22
 p-value of test no 254                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35797
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 16                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 23                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 28                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 29                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 39                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.50
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.56
 p-value of test no 47                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.10
 p-value of test no 48                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.82
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.05
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.38
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.81
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.61
 p-value of test no 54                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.12
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.19
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.73
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 59                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.85
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 64                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.44
 p-value of test no 65                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.15
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.10
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.57
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45987
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869987
   j =  1                              :        399908028
   j =  2                              :            45983
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908283
   j =  2                              :            45857
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 76                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 77                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 90                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 91                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 94                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 100                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 103                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.42
 p-value of test no 115                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.92
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.58
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.95
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.49
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.78
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.74
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.95
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.99
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.15
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 138                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.24
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 142                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17660.81
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.71
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.00
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.68
 p-value of test no 149                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.53
 p-value of test no 150                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.74
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.99
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.68
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.67
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.24
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.89
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.47
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.56
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.11
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.26
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.80
 p-value of test no 161                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.70
 p-value of test no 162                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.78
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.96
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  118.49
 p-value of test no 165                :  7.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.48
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.96
 p-value of test no 167                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.66
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.64
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.97
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  447.57
 p-value of test no 171                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.86
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.78
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.74
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.39
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.69
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.50
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.88
 p-value of test no 178                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.82
 p-value of test no 188                :    0.97
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
 p-value of test no 190                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.63
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.86
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.99
 p-value of test no 203                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.02
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10099.46
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.01e-3
 p-value of test no 212                :    0.9979
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 213                :  5.1e-4    *****
 
 Anderson-Darling statistic = A2       :    5.22
 p-value of test no 214                :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10435.89
 p-value of test no 215                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.02
 p-value of test no 216                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 221                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.03
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4854.92
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3898.76
 p-value of test no 227                :    0.9927
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.69
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.84
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12087.60
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.68
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000085894
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 232                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   81.47
 p-value of test no 233                :  9.2e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999922574
 
 Normal statistic for number of bits   :   -0.61
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.69
 p-value of test no 244                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.43
 p-value of test no 254                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:45.48
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    7.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35798
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 8                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 11                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4163
 p-value of test no 16                 :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7404
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.15
 p-value of test no 26                 :    0.9984
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.23
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 36                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.65
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.35
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.27
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.76
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.09
 p-value of test no 49                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.53
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.76
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.02
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.69
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.87
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.86
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.49
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7254.47
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.19
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.67
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.76
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.58
 p-value of test no 67                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4904.90
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45713
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869713
   j =  1                              :        399908580
   j =  2                              :            45701
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46227
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870227
   j =  1                              :        399907549
   j =  2                              :            46221
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 92                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 101                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    3.41
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 108                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.086
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 117                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   97.27
 p-value of test no 120                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.93
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.86
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.44
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.66
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.19
 p-value of test no 125                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.13
 p-value of test no 129                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.49
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.49
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.85
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.71
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.35
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.21
 p-value of test no 147                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.59
 p-value of test no 148                :    0.9947
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.65
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.39
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.86
 p-value of test no 151                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.40
 p-value of test no 152                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.22
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.99
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.08
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.55
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.38
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.43
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.68
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.06
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  210.09
 p-value of test no 161                :  4.1e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.85
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.57
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.84
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.09
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.96
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.64
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.38
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.84
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.86
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.02
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.62
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.86
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  313.43
 p-value of test no 174                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.05
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.08
 p-value of test no 176                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.45
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.96
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 183                :    0.76
 
 Sample variance                       :    2.29
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.71
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.69
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 3.64e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.83
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.75
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.83
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.15
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.14
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.01
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.67
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.05
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.41
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.22
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.20
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.13
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11647.66
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.84
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000026221
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.36
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000026137
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 236                :    0.9967
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.25
 p-value of test no 238                :    0.99
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.041
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.87
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 H (L=1000, r=20)    4.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35799
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4419
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4270
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7538
 p-value of test no 19                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.49
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     863
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9957
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     578
 p-value of test no 31                 :    0.81
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 45                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.17
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.46
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.99
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.27
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   29.99
 p-value of test no 51                 :    0.9967
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.52
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.23
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  217.42
 p-value of test no 54                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.26
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.64
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7146.91
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.93
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.00
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.10
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5193.76
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46217
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870217
   j =  1                              :        399907568
   j =  2                              :            46213
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45877
 p-value of test no 71                 :    0.50
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869877
   j =  1                              :        399908251
   j =  2                              :            45867
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 72                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 79                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 80                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    5.56
 p-value of test no 81                 :  1.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :  1.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-4
 p-value of test no 84                 :    0.9996    *****
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.24
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 107                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 108                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.53
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 119                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.74
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.41
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.34
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.73
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.57
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.74
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.50
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.07
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.24
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 137                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 140                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.36
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17321.79
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.85
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.93
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.19
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.52
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.52
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.18
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.80
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.00
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.50
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.27
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.09
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.92
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.51
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.55
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.56
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.24
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.85
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.55
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.16
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.17
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.66
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5038.33
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.38
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.74
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.23
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.14
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.12
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.64
 p-value of test no 174                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.07
 p-value of test no 175                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.22
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.49
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    2.13
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-3
 p-value of test no 191                :    0.99
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 192                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.10
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.28
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.61
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10178.81
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 213                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.55
 p-value of test no 214                :  5.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10374.44
 p-value of test no 215                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.64
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4971.45
 p-value of test no 226                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4301.12
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.83
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11716.99
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.99
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.41
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000218776
 
 Normal statistic for number of bits   :    1.73
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.74
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999903401
 
 Normal statistic for number of bits   :   -0.76
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 243                :    0.84
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.92
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.79
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.75
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:51.23
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35800
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 6                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 7                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7156
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.72
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 32                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 41                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.59
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.29
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.47
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.55
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.49
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.72
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.09
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.80
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.51
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.01
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7254.36
 p-value of test no 57                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.35
 p-value of test no 61                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.55
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.25
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.15
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4879.43
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908064
   j =  2                              :            45962
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907967
   j =  2                              :            46015
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 83                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 85                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 88                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 111                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.37
 p-value of test no 119                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.51
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.25
 p-value of test no 121                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.04
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.76
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.03
 p-value of test no 124                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.67
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 126                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.64
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.25
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.57
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.81
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.94
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.40
 p-value of test no 147                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.54
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.64
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.88
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.48
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.71
 p-value of test no 152                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.20
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.50
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.43
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.68
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.47
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.53
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.23
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.32
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.27
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.61
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.13
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.72
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.92
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.17
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5001.15
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.82
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.01
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.62
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.05
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.95
 p-value of test no 173                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.95
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.58
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.97
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.61
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 185                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.11
 p-value of test no 196                :    0.85
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.60
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.46
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.18
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.44
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.56
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 218                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4858.24
 p-value of test no 222                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.84
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.47
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4256.57
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.73
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11922.38
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.84
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999945608
 
 Normal statistic for number of bits   :   -0.43
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   85.14
 p-value of test no 233                :  4.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999920204
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 238                :    0.36
 
 Sample variance                       :    2.29
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.94
 p-value of test no 244                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.70
 p-value of test no 248                :    0.05
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 253                :    0.64
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:57.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35801
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 6                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 16                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4461
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7469
 p-value of test no 19                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 20                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7183
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 30                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     570
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.57
 p-value of test no 35                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 38                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 39                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.23
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.54
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.75
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.09
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.41
 p-value of test no 50                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.96
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.25
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.22
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.53
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.68
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1433.06
 p-value of test no 56                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.79
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 59                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 60                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.43
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 63                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.43
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.24
 p-value of test no 66                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.88
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4975.96
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45723
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869723
   j =  1                              :        399908559
   j =  2                              :            45713
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46076
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870076
   j =  1                              :        399907855
   j =  2                              :            46062
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 78                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 86                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 99                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 102                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.62
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.58e-5
 p-value of test no 112                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.48
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.34
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.88
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.10
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.79
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.30
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.69
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 126                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.15
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.04
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.82
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.61
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.14
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 144                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17510.42
 p-value of test no 145                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.86
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.00
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.35
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.43
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.36
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.76
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.37
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.32
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.27
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.12
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.30
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  430.49
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.66
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.83
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.51
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.02
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.91
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.16
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   39.78
 p-value of test no 165                :    0.9996    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.54
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  462.14
 p-value of test no 167                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4897.28
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.71
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.21
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.15
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.61
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4844.68
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.96
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.89
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.78
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.12
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.06
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.94
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 188                :    0.82
 
 Sample variance                       :    0.93
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.64
 p-value of test no 196                :    0.9902
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.54
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.82
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.33
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9986.00
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.53
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 217                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 220                :    0.80
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.29
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.04
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.97
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4011.75
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.82
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.99
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.17
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  7999951968
 
 Normal statistic for number of bits   :   -0.38
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.45
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000017929
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 242                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 248                :    0.58
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.46e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:22.31
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 C (L=1000, r=20)    0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35802
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 3                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 10                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5402
 p-value of test no 13                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 15                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4186
 p-value of test no 17                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 18                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7391
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 21                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 22                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 23                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 24                 :    0.9967
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.87
 p-value of test no 35                 :  3.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.19
 p-value of test no 47                 :    0.9912
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.06
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.89
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.83
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.09
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.54
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  483.71
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.91
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6893.52
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.17
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.72
 p-value of test no 65                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.37
 p-value of test no 67                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5143.51
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45972
 p-value of test no 70                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869972
   j =  1                              :        399908058
   j =  2                              :            45968
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45681
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908644
   j =  2                              :            45669
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 74                 :    0.9934
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 88                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 93                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 99                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 101                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 104                :    0.94
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 107                :  2.9e-3
 
 Anderson-Darling statistic = A2       :    4.81
 p-value of test no 108                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
 p-value of test no 109                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    4.18
 p-value of test no 111                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 114                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.64
 p-value of test no 119                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.93
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.49
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.93
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.12
 p-value of test no 123                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.45
 p-value of test no 124                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.33
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.08
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.70
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17277.55
 p-value of test no 145                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.33
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.56
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.83
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.92
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.95
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.21
 p-value of test no 151                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.02
 p-value of test no 152                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.57
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.81
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.47
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.64
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.22
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.35
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.11
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.91
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.02
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.31
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.78
 p-value of test no 163                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.12
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.63
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.52
 p-value of test no 166                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.62
 p-value of test no 167                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.64
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.48
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.92
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.50
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.43
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.42
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.73
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.89
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.58
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.31
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 179                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.49
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 182                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    0.30
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.08
 p-value of test no 196                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.86
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.40
 p-value of test no 203                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 205                :    0.01
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.62
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9869.65
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10045.62
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.25
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.61
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.69
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.34
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.72
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11899.82
 p-value of test no 230                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.75
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000102805
 
 Normal statistic for number of bits   :    0.81
 p-value of test no 232                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.57
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999998993
 
 Normal statistic for number of bits   : -7.96e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 237                :    0.9959
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.068
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 247                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.19
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 253                :    0.23
 
 Sample variance                       :    2.10
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:18.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35803
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 4                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 8                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5228
 p-value of test no 13                 :    0.9957
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4187
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    4.65
 p-value of test no 32                 :  4.2e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.76
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.77
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.77
 p-value of test no 50                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.97
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.29
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.01
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.01
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  489.96
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.50
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7038.44
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.57
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.60
 p-value of test no 65                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.47
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.52
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45850
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869850
   j =  1                              :        399908302
   j =  2                              :            45846
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45765
 p-value of test no 71                 :    0.70
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869765
   j =  1                              :        399908472
   j =  2                              :            45761
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 79                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 97                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 108                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.23
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.90
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.80
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.71
 p-value of test no 122                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.16
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.19
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 127                :  5.0e-3
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 128                :  9.2e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   66.07
 p-value of test no 129                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.39
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.51
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.66
 p-value of test no 141                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17612.33
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.44
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.91
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.74
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.90
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.50
 p-value of test no 150                :  9.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.92
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.20
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.20
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.25
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.81
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.38
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.76
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  584.71
 p-value of test no 158                :  5.2e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.33
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.47
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  197.44
 p-value of test no 161                :  2.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.75
 p-value of test no 162                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.39
 p-value of test no 163                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.30
 p-value of test no 164                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.48
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.94
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.99
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.89
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.64
 p-value of test no 169                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.11
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.63
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.47
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.04
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.49
 p-value of test no 174                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  169.65
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.84
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.35
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.84
 p-value of test no 178                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :-1.40e-16
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
 p-value of test no 194                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.04
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.17
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.77
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.28
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10097.30
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 213                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 214                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.62
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.061
 p-value of test no 216                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.29
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.00
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.55
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3978.83
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4273.25
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11986.42
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.69
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.74
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999956339
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.09
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000018034
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 236                :    0.06
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.81
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.079
 p-value of test no 248                :    0.47
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:03.11
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35804
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 6                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 7                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 11                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5405
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7440
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7314
 p-value of test no 20                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 26                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.38
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     614
 p-value of test no 31                 :    0.29
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 33                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    5.38
 p-value of test no 34                 :  2.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 39                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.10
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.49
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.09
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.90
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.75
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.27
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.81
 p-value of test no 52                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.94
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.22
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1455.26
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7179.68
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.16
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.97
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.03
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.36
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.33
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45782
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869782
   j =  1                              :        399908442
   j =  2                              :            45770
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45938
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869938
   j =  1                              :        399908128
   j =  2                              :            45930
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 73                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 76                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 83                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 87                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 88                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 90                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.18
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 102                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 117                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.43
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.97
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.05
 p-value of test no 121                :    0.9964
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.10
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.41
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.92
 p-value of test no 124                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.19
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.81
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 132                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.92
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.66
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.96
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.48
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.69
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.27
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.96
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.41
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.07
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.48
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.67
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.12
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.64
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.01
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.59
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.52
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.67
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.80
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.85
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.21
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.23
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.08
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.32
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.53
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.01
 p-value of test no 165                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.89
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.03
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.11
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.22
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.49
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.54
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.35
 p-value of test no 173                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.17
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.95
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.48
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.46
 p-value of test no 179                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 183                :    0.13
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 188                :    0.74
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 191                :    0.83
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 194                :    0.88
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.18
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.94
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.59
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 206                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.13
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10164.95
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.95
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4884.35
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.26
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4252.42
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.75
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.06
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12022.68
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.18
 p-value of test no 231                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000003676
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.07
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000016087
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.12
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.66
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 243                :    0.20
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.23
 
 Sample variance                       :    1.61
 p-value of test no 249                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 251                :    0.88
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 253                :    0.82
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:47.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35805
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 4                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 8                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5505
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7569
 p-value of test no 15                 :  1.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4274
 p-value of test no 17                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 18                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7417
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.83
 p-value of test no 23                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     945
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 36                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.72
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.22
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.43
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.43
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.34
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.74
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.78
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  484.32
 p-value of test no 55                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1485.27
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6968.86
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 59                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.20
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.46
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.85
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.75
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5045.90
 p-value of test no 68                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45903
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869903
   j =  1                              :        399908196
   j =  2                              :            45899
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907970
   j =  2                              :            46015
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 81                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 92                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 97                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.33
 p-value of test no 115                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.51
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.47
 p-value of test no 120                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.15
 p-value of test no 121                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.76
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.37
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.42
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 128                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.71
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.26
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.18
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.12
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17744.17
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.50
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.60
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.64
 p-value of test no 149                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.53
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.40
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.80
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.60
 p-value of test no 154                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.85
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.11
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.29
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.42
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.82
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.89
 p-value of test no 160                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.50
 p-value of test no 161                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.99
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.33
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.41
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.99
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.40
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.28
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.33
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.90
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.70
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.47
 p-value of test no 172                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4975.60
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.09
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.81
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.57
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.67
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.03
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.22
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.74
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.20
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9873.21
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.01
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 221                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.66
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5044.52
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4023.46
 p-value of test no 227                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.80
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.84
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11611.34
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.70
 p-value of test no 231                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000037033
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.04
 p-value of test no 233                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999841391
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 238                :    0.22
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.53
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.87
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.62
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:06.35
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35806
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 4                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5272
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4286
 p-value of test no 14                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7509
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.01
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     833
 p-value of test no 25                 :    0.99
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.55
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    2.27
 p-value of test no 32                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.55
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.66
 p-value of test no 49                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.13
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.56
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.47
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.76
 p-value of test no 53                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.23
 p-value of test no 54                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  506.53
 p-value of test no 55                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1538.41
 p-value of test no 56                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7155.67
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.45
 p-value of test no 61                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.06
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.19
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.89
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.60
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45849
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869849
   j =  1                              :        399908305
   j =  2                              :            45843
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908893
   j =  2                              :            45546
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 74                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 85                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 98                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 104                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.39e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
 p-value of test no 112                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.23
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.79
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.44
 p-value of test no 122                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.84
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.94
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.15
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.79
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.61
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.97
 p-value of test no 134                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.03
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.89
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.25
 p-value of test no 146                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.75
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.61
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.98
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.91
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.36
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.99
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.87
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.76
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.49
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.30
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.12
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.28
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.12
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.95
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.23
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.92
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.29
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.69
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.09
 p-value of test no 168                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.74
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.84
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.58
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.95
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.78
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.03
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.85
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.57
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.69
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.28
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.3e-3
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.56
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.01
 p-value of test no 184                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 196                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.59
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.48
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.29
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 209                :    0.77
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.11
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.65
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 216                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 219                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4983.78
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4699.78
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4285.46
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4015.97
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.07
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.28
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.79
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999995144
 
 Normal statistic for number of bits   :  -0.038
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.00
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000020374
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.54
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.46
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 242                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:45.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35807
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  6.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 8                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1276
 p-value of test no 11                 :    0.9917
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334396
   j =  1                              :        599997448
   j =  2                              :             1276
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5416
 p-value of test no 13                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 21                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 28                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    3.21
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 39                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     132
 p-value of test no 43                 :    0.93
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.52
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.65
 p-value of test no 47                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.50
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.77
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.70
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.38
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.49
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.74
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  250.77
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.63
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.16
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7194.91
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.81
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.92
 p-value of test no 65                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.16
 p-value of test no 67                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.68
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908694
   j =  2                              :            45650
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45962
 p-value of test no 71                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869962
   j =  1                              :        399908079
   j =  2                              :            45956
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.42e-3
 p-value of test no 83                 :    0.9974
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 86                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.08e-6
 p-value of test no 112                :    0.9980
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.11
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.61
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.45
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.98
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.98
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.74
 p-value of test no 123                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.69
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.15
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 128                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.42
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.35
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.52
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.88
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.93
 p-value of test no 136                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.51
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 144                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17110.24
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.51
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.86
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.80
 p-value of test no 148                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.10
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.26
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.49
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.98
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.39
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.87
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.75
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.59
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.97
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.90
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.88
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.39
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.62
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.62
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.45
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.71
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.22
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.37
 p-value of test no 166                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.21
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.88
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.37
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.19
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.25
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.92
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.38
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.22
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.10
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.60
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.08
 p-value of test no 177                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.58
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 182                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    2.08
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.38
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.18
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 202                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.94
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.74
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.30
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 209                :    0.91
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 210                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9894.69
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9969.81
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.52
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.49
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.68
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.92
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4040.31
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11948.42
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.57
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.64
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999942896
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 232                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.51
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999803180
 
 Normal statistic for number of bits   :   -1.56
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 237                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.64
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 253                :    0.80
 
 Sample variance                       :    1.03
 p-value of test no 254                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:24.19
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35808
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7180
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 17                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 26                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.40
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     270
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.21
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    3.13
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.06
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.47
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.16
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.28
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.69
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.42
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.49
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.26
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.96
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.60
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1403.13
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7180.23
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.12
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.28
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.20
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.31
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5007.90
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.64e+6
 p-value of test no 69                 :  2.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45737
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869737
   j =  1                              :        399908529
   j =  2                              :            45731
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45398
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869398
   j =  1                              :        399909210
   j =  2                              :            45386
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 72                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 81                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 107                :    0.76
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 111                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 112                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-5
 p-value of test no 113                :    0.82
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.98
 p-value of test no 118                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.52
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.84
 p-value of test no 120                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.74
 p-value of test no 121                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.04
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.56
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.48
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.52
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.17
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 131                :    0.82
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.61
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.74
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.46
 p-value of test no 137                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.35
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17570.52
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.60
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.40
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.26
 p-value of test no 148                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.62
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.05
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.19
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.61
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.26
 p-value of test no 153                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.19
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.45
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.89
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.89
 p-value of test no 158                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.12
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.13
 p-value of test no 160                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.41
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.91
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.65
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.55
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.63
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.10
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.26
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.00
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.55
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.32
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.79
 p-value of test no 171                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  461.57
 p-value of test no 172                :  4.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.18
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  315.53
 p-value of test no 174                :    0.9915
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.72
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.29
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.21
 p-value of test no 177                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.96
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.99
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 182                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.69
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.37
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.05
 p-value of test no 196                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.46
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.40
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.61
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.32
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10009.88
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.68
 p-value of test no 216                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.54
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.07
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.72
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.09
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11499.80
 p-value of test no 229                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11897.09
 p-value of test no 230                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.21
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999909761
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.34
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000078082
 
 Normal statistic for number of bits   :    0.62
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.83
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.38
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.25
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 252                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:00.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35809
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 11                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7070
 p-value of test no 19                 :    0.9982
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     853
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 28                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    2.04
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 35                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 40                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.39
 p-value of test no 44                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.08
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.08
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.65
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.74
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.66
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.07
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.16
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  455.14
 p-value of test no 55                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1449.11
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6911.80
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.24
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.03
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.88
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.69
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5044.02
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908005
   j =  2                              :            45993
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908698
   j =  2                              :            45645
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 76                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.04
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 88                 :    0.9902
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.62
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.032
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 119                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.74
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.59
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.15
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.67
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.14
 p-value of test no 125                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.37
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.82
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.84
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.64
 p-value of test no 135                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.99
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17298.38
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.82
 p-value of test no 147                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.22
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.92
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.06
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.10
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.62
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.06
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.04
 p-value of test no 154                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.86
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.75
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.05
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.87
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.68
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.40
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.34
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.08
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.36
 p-value of test no 164                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.43
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.07
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.96
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.23
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.93
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.06
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.03
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.28
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.48
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.12
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.16
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.90
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.98
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.05
 p-value of test no 179                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 183                :    0.25
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 188                :    0.62
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.30
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.00
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 202                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.66
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.16
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.00
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10210.28
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 213                :    0.02
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10135.05
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.97
 p-value of test no 217                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.52
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4777.53
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 225                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5134.06
 p-value of test no 226                :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.31
 p-value of test no 227                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.45
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11699.65
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11907.29
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.65
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999973586
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.69
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000020698
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 238                :    0.62
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.94
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:58.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35810
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 12                 :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7191
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.39
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     901
 p-value of test no 25                 :    0.49
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.72
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.17
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    3.65
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.50
 p-value of test no 42                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.44
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.87
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.36
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.78
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.28
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.31
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.74
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1561.82
 p-value of test no 56                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.49
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 60                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.04
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.22
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.57
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.74
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45595
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869595
   j =  1                              :        399908811
   j =  2                              :            45593
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908335
   j =  2                              :            45831
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 78                 :    0.9990
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 80                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 87                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 93                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.03
 
 Anderson-Darling statistic = A2       :    2.83
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 105                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 106                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.26
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.63
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.11
 p-value of test no 121                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.12
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.51
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.00
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.32
 p-value of test no 125                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.67
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.72
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.68
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.37
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 136                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   91.35
 p-value of test no 141                :    0.9959
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.78
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.94
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.16
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.71
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.93
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.22
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.79
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.91
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.24
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.28
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.55
 p-value of test no 159                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.31
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.52
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.66
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.60
 p-value of test no 163                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.41
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.84
 p-value of test no 165                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.72
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.67
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5047.46
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.55
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.06
 p-value of test no 170                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.64
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.56
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5106.41
 p-value of test no 173                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.81
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.66
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.49
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.18
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 183                :    0.43
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 188                :    0.61
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 193                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.20
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 195                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.68
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.28
 p-value of test no 198                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.82
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.16
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.13
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.40
 p-value of test no 211                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.66
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.39
 p-value of test no 218                :    0.9915
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.15
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.15
 p-value of test no 226                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.65
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.24
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.37
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.88
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.07
 p-value of test no 231                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000014734
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999988133
 
 Normal statistic for number of bits   :  -0.094
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 248                :    0.42
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.031
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:55.63
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35811
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 6                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5612
 p-value of test no 13                 :  5.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4357
 p-value of test no 16                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 18                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7407
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 21                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 22                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 23                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 26                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 28                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    2.68
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 42                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     170
 p-value of test no 43                 :    0.06
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.78
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.03
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.57
 p-value of test no 48                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.47
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.77
 p-value of test no 50                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.28
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.57
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.94
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.95
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1490.80
 p-value of test no 56                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7066.39
 p-value of test no 57                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.84
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 63                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.15
 p-value of test no 65                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.56
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.91
 p-value of test no 67                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.06
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46110
 p-value of test no 70                 :    0.14
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870110
   j =  1                              :        399907787
   j =  2                              :            46096
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46394
 p-value of test no 71                 :  8.3e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870394
   j =  1                              :        399907219
   j =  2                              :            46380
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 95                 :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 98                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 100                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.38
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
 p-value of test no 109                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.04e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 114                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.065
 p-value of test no 116                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.44
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.11
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.72
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.71
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.38
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.19
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.99
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.21
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.12
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17136.60
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.20
 p-value of test no 146                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.64
 p-value of test no 147                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.47
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.48
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.36
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.64
 p-value of test no 151                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.46
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.29
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.08
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.17
 p-value of test no 155                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.09
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.79
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.51
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.77
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.65
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.07
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.90
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.14
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.16
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.52
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.49
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.26
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4802.25
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.76
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.82
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.56
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.39
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.65
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.85
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.45
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.43
 p-value of test no 176                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.54
 p-value of test no 178                :  9.0e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.13
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 182                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 183                :    0.73
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
 p-value of test no 190                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 191                :    0.02
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.26
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.51
 p-value of test no 198                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.46
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.56
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.42
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 213                :    0.9924
 
 Anderson-Darling statistic = A2       :    3.36
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9641.47
 p-value of test no 215                :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.33
 p-value of test no 216                :  9.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.076
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 220                :    0.83
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.85
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.57
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4242.04
 p-value of test no 227                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.91
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.36
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11712.13
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.77
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999977321
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.74
 p-value of test no 233                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999869441
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 245                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.08
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.47
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.49
 p-value of test no 253                :    0.31
 
 Sample variance                       :    0.73
 p-value of test no 254                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:20.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35812
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 10                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4290
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.41
 p-value of test no 40                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 42                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.01
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    0.92
 p-value of test no 47                 :    0.9960
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.42
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.82
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.62
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.03
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.43
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.60
 p-value of test no 53                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.82
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  466.35
 p-value of test no 55                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.76
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7163.53
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.71
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.62
 p-value of test no 65                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.83
 p-value of test no 67                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5248.20
 p-value of test no 68                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908008
   j =  2                              :            45990
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45763
 p-value of test no 71                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869763
   j =  1                              :        399908476
   j =  2                              :            45759
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 88                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 99                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
 p-value of test no 112                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 117                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.92
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.49
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.93
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.62
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.48
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.08
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.98
 p-value of test no 125                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.92
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.93
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.92
 p-value of test no 134                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.27
 p-value of test no 136                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 140                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.86
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 143                :    0.81
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17342.01
 p-value of test no 145                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.58
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.20
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.89
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.23
 p-value of test no 149                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.49
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.13
 p-value of test no 151                :    0.9905
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.32
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.63
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.76
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.41
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.46
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.28
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.10
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.05
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  175.60
 p-value of test no 161                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.49
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.78
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.80
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.50
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.52
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.17
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.88
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.23
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.31
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.58
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.56
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.66
 p-value of test no 173                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.05
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.12
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.48
 p-value of test no 176                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.14
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.22
 p-value of test no 183                :    0.89
 
 Sample variance                       :    1.54
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.74
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  174.10
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.38
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 209                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.02
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-4
 p-value of test no 213                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9685.75
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 217                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 219                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.48
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4808.24
 p-value of test no 226                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.10
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4067.22
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11757.96
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.71
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.91
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999942158
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.75
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000183469
 
 Normal statistic for number of bits   :    1.45
 p-value of test no 234                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 235                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 243                :    0.70
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 248                :    0.46
 
 Sample variance                       :    2.74
 p-value of test no 249                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 252                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.015
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.80
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:12.75
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35813
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 12                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5376
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 22                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.26
 p-value of test no 23                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     947
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.04
 p-value of test no 33                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 39                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    2.09
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.21
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.65
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.78
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.06
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.44
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.01
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.39
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.04
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.38
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  344.72
 p-value of test no 55                 :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1530.24
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7025.13
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.42
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 63                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.17
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.86
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.47
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4901.60
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45577
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869577
   j =  1                              :        399908851
   j =  2                              :            45567
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45733
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869733
   j =  1                              :        399908537
   j =  2                              :            45727
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 73                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 84                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 100                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 106                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.80
 p-value of test no 120                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.99
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.10
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.19
 p-value of test no 124                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.32
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.54
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 130                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.80
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.38
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 137                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.22
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.49
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.93
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.10
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.08
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.75
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.75
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.22
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.15
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.82
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.28
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.57
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.94
 p-value of test no 156                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.15
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.34
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.39
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.04
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.28
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.21
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.05
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.96
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.14
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.86
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.27
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5192.42
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.12
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  247.74
 p-value of test no 170                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.65
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.29
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.86
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.10
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.01
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.30
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.94
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 179                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 183                :    0.06
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.45
 p-value of test no 189                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
 p-value of test no 190                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 195                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.40
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.70
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.91
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.69
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 208                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10048.61
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 212                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9714.26
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.12
 p-value of test no 222                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.67
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.62
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.69
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12079.43
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.65
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.50
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000005266
 
 Normal statistic for number of bits   :   0.042
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.47
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  8000026641
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.53
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 238                :    0.45
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 240                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.43
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 251                :    0.9929
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.94
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.18
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:51.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  35  Gap, r = 25                     0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35814
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 3                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 4                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 7                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5466
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4253
 p-value of test no 16                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 17                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 18                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 23                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.83
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    1.88
 p-value of test no 36                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     326
 p-value of test no 37                 :    0.07
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    3.56
 p-value of test no 39                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 40                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 41                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.85
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.42
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.00
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.22
 p-value of test no 49                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.03
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.60
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.38
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.68
 p-value of test no 53                 :    0.9904
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.15
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.31
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.78
 p-value of test no 56                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7120.45
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.48
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.32
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.56
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.97
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5039.34
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908926
   j =  2                              :            45534
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45513
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869513
   j =  1                              :        399908979
   j =  2                              :            45503
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 73                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.80
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 92                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 105                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 111                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.16
 p-value of test no 116                :  7.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 118                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.99
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.28
 p-value of test no 120                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.74
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.94
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.02
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.49
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.69
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.56
 p-value of test no 129                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.95
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.31
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.14
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.94
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.48
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.38
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 144                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17533.12
 p-value of test no 145                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.29
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.73
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.38
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.63
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.65
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.04
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.12
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.00
 p-value of test no 153                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.65
 p-value of test no 154                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.13
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.51
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.51
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.78
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.15
 p-value of test no 159                :    0.9925
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.46
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.54
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.51
 p-value of test no 162                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.08
 p-value of test no 163                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.82
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.69
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.75
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.26
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.81
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.42
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.18
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.60
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.73
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.12
 p-value of test no 173                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.54
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.39
 p-value of test no 175                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.68
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.30
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.47
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 183                :    0.30
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.72
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.05
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.38e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.91
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 202                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.80
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 204                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.82
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 209                :    0.06
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.20
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.25
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.053
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.30
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4911.75
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.33
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4126.66
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.64
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12058.34
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.77
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.96
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999937025
 
 Normal statistic for number of bits   :   -0.50
 p-value of test no 232                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.23
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  7999836132
 
 Normal statistic for number of bits   :   -1.30
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 238                :    0.25
 
 Sample variance                       :    1.32
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.10
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.85
 p-value of test no 249                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.47
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:51.43
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               7.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35815
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 4                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1461
 p-value of test no 11                 :  4.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334581
   j =  1                              :        599997078
   j =  2                              :             1461
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 23                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     574
 p-value of test no 31                 :    0.85
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9923
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 35                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 36                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 38                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 39                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    4.13
 p-value of test no 44                 :  7.5e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.46
 p-value of test no 46                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.07
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.34
 p-value of test no 49                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.41
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.97
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.42
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.48
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.56
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1469.39
 p-value of test no 56                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6881.63
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.59
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
 p-value of test no 62                 :    0.9986
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   96.12
 p-value of test no 65                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.89
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.55
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.28
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908524
   j =  2                              :            45738
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45653
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869653
   j =  1                              :        399908695
   j =  2                              :            45651
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 80                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 88                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.30
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 102                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 107                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
 p-value of test no 109                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
 p-value of test no 112                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.64
 p-value of test no 118                :    0.9958
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.98
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.04
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.74
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.05
 p-value of test no 123                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.58
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.21
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.21
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.07
 p-value of test no 135                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.93
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.51
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 144                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17524.09
 p-value of test no 145                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.55
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.45
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.42
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.77
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.87
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.41
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.61
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.67
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.20
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.09
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.46
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.80
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  192.78
 p-value of test no 162                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.51
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.68
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.79
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.33
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.17
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4872.95
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.59
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.44
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.84
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.73
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.08
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.82
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.34
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 177                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.60
 p-value of test no 178                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.64
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.33
 p-value of test no 198                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 202                :    0.9939
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.00
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.94
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 209                :    0.99
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.63
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.85
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.49
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 221                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.26
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 224                :    0.82
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.23
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.36
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4185.58
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.40
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11819.00
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.25
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000020485
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.46
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000074731
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.52
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 248                :    0.53
 
 Sample variance                       :    0.51
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:13.28
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35816
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 4                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 7                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 9                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 14                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7247
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 24                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     559
 p-value of test no 31                 :    0.95
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.26
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     271
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 41                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.24
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     184
 p-value of test no 43                 :  4.0e-3
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 44                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.16
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.38
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.20
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.01
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.16
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.30
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.60
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7213.68
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.65
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.70
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.11
 p-value of test no 66                 :    0.9998    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.74
 p-value of test no 67                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.21
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45759
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869759
   j =  1                              :        399908486
   j =  2                              :            45751
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46440
 p-value of test no 71                 :  4.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870440
   j =  1                              :        399907123
   j =  2                              :            46434
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 90                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 97                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.26
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
 p-value of test no 109                :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.84e-6
 p-value of test no 110                :    0.9961
 
 Anderson-Darling statistic = A2       :    6.75
 p-value of test no 111                :  4.4e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.59
 p-value of test no 116                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 118                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.94
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.61
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.58
 p-value of test no 121                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.89
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.99
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.69
 p-value of test no 125                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.58
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.20
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 134                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.58
 p-value of test no 135                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.11
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17675.57
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.10
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.51
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.71
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.95
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.50
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.69
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.25
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.35
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.54
 p-value of test no 154                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.23
 p-value of test no 155                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.13
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.56
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.96
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.21
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.93
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.52
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.55
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.00
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.51
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.70
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.75
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.63
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5152.75
 p-value of test no 168                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.16
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.53
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.31
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.41
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.30
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.00
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.01
 p-value of test no 175                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.06
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.95
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.43
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.19
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.84
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.44
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9781.94
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 213                :    0.83
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.35
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 216                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.20
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.33
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 225                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.62
 p-value of test no 226                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.27
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.69
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.62
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11715.64
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000036643
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.05
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999910130
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 235                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 238                :    0.98
 
 Sample variance                       :    2.21
 p-value of test no 239                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 243                :    0.47
 
 Sample variance                       :    0.85
 p-value of test no 244                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.58
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 253                :    0.44
 
 Sample variance                       :    1.97
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:07.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              0.9998 
  53  SampleMean, r = 0               4.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35817
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 8                  :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 19                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 20                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7120
 p-value of test no 21                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.20
 p-value of test no 22                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 32                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.44
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.07
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.43
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.57
 p-value of test no 48                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.24
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.64
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.21
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.42
 p-value of test no 52                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   27.22
 p-value of test no 53                 :    0.9991    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.49
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.88
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.48
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.28
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.24
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.60
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.56
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.18
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.55
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46165
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870165
   j =  1                              :        399907671
   j =  2                              :            46163
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45826
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869826
   j =  1                              :        399908351
   j =  2                              :            45820
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 95                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.49
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.45
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.18
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.87
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.52
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.47
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 126                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.63
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.00
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.41
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.16
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.73
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.06
 p-value of test no 146                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.41
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.42
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.31
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.66
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.15
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.50
 p-value of test no 152                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.47
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.02
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.38
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.41
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.74
 p-value of test no 158                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  105.98
 p-value of test no 159                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.61
 p-value of test no 160                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.87
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.93
 p-value of test no 162                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.57
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.72
 p-value of test no 164                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.12
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.15
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.30
 p-value of test no 167                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.03
 p-value of test no 168                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.11
 p-value of test no 169                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.88
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.30
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.51
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.16
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.04
 p-value of test no 174                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.60
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.77
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 187                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 188                :    0.07
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.41
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.39
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 200                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  166.75
 p-value of test no 203                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.47
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.28
 p-value of test no 207                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.36
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.61
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.92
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.74
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 223                :  7.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 225                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.22
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.02
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.89
 p-value of test no 228                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11864.10
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11684.37
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.95
 p-value of test no 231                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000026842
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.37
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999949184
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.05
 p-value of test no 238                :    0.85
 
 Sample variance                       :    1.36
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 240                :  3.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.15
 p-value of test no 244                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 245                :  5.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    4.20
 p-value of test no 247                :  7.3e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.36
 p-value of test no 248                :    0.9908
 
 Sample variance                       :    0.29
 p-value of test no 249                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.04
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 253                :    0.07
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:54.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  33  CouponCollector, r = 27         0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35818
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 11                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 14                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7230
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.78
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 32                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 33                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.38
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.42
 p-value of test no 41                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    1.56
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.08
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 47                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.90
 p-value of test no 48                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.13
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.55
 p-value of test no 50                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.46
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.40
 p-value of test no 52                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.68
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.70
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.40
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1488.78
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7285.82
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 58                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.54
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   69.85
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.69
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5162.32
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46326
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870326
   j =  1                              :        399907353
   j =  2                              :            46316
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45691
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869691
   j =  1                              :        399908622
   j =  2                              :            45683
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.55
 p-value of test no 81                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9960
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 87                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 92                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 95                 :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 106                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 107                :  4.6e-4    *****
 
 Anderson-Darling statistic = A2       :    6.90
 p-value of test no 108                :  3.9e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-6
 p-value of test no 109                :    0.9985
 
 Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.47
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.11
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.62
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.84
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.51
 p-value of test no 123                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.95
 p-value of test no 124                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.58
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 126                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.62
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 131                :    0.99
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.54
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.22
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 139                :    0.93
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.54
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17508.42
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.32
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.50
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.52
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.74
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.37
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.15
 p-value of test no 151                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.48
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.33
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.78
 p-value of test no 154                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.94
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.79
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.86
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.95
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.16
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.38
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.94
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.00
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.23
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.68
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.44
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.12
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.57
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4981.60
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.98
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.56
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.84
 p-value of test no 171                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.81
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.43
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.62
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.44
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.96
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.13
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.39
 p-value of test no 184                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 185                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.28
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 187                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.42
 p-value of test no 189                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 195                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.88
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.97
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.29
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.18
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9995.38
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.71
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.054
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 221                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.84
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.22
 p-value of test no 226                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.53
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.10
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.22
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.82
 p-value of test no 230                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   40.84
 p-value of test no 231                :    0.91
 
 
 -----------------------------------------------
 Total number of bits:  8000037402
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.82
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000029044
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.94
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.053
 p-value of test no 253                :    0.48
 
 Sample variance                       :    1.24
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:39.26
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  52  SampleProd, t = 24              3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35819
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 4                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 5                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 6                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 11                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7496
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4164
 p-value of test no 17                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 19                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7441
 p-value of test no 21                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.88
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 23                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    2.93
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     981
 p-value of test no 25                 :  4.0e-3
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     629
 p-value of test no 31                 :    0.12
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 33                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     334
 p-value of test no 37                 :    0.03
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 45                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.95
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.45
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.06
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.73
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.94
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.42
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.98
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.93
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.77
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  367.46
 p-value of test no 55                 :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.99
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6979.50
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.85
 p-value of test no 61                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 64                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.19
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.02
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.35
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.88
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907973
   j =  2                              :            46009
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 71                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907800
   j =  2                              :            46091
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.27
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9928
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
 p-value of test no 77                 :    0.9946
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 78                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 81                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 98                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 111                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 116                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 117                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.46
 p-value of test no 118                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.27
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.33
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.72
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.66
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.24
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.99
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.31
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 128                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.58
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.56
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.25
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.59
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 136                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.75
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17138.83
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.49
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.94
 p-value of test no 148                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.04
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.36
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.02
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.27
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.62
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.34
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.99
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.26
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.95
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.97
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.64
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.94
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.25
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.05
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.76
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.51
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.61
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.87
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.96
 p-value of test no 169                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.17
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.04
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.66
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4865.70
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.06
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.90
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.75
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.74
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 183                :    0.41
 
 Sample variance                       :    0.37
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 188                :    0.19
 
 Sample variance                       :    1.50
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 195                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.56
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.87
 p-value of test no 207                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.29
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9888.33
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.05
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.77
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 218                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.91
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 224                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.34
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4290.08
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4200.46
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.28
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12038.47
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.00
 p-value of test no 231                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999868928
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.77
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999851135
 
 Normal statistic for number of bits   :   -1.18
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
 p-value of test no 235                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.82
 p-value of test no 238                :    0.03
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.98
 p-value of test no 243                :    0.16
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.03
 p-value of test no 253                :    0.98
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:30.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35820
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 12                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5493
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.90
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 24                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 34                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 35                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    2.43
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     259
 p-value of test no 37                 :    0.9914
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.98
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 45                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.40
 p-value of test no 46                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.26
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.85
 p-value of test no 48                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.88
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.67
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 51                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.76
 p-value of test no 53                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.28
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.45
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.94
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7121.68
 p-value of test no 57                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.51
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.05
 p-value of test no 65                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.58
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.95
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5146.37
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45652
 p-value of test no 70                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869652
   j =  1                              :        399908697
   j =  2                              :            45650
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46352
 p-value of test no 71                 :    0.01
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870352
   j =  1                              :        399907297
   j =  2                              :            46350
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
 p-value of test no 107                :    0.9928
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-5
 p-value of test no 113                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 117                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -8.68e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.99
 p-value of test no 119                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.81
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.92
 p-value of test no 121                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.92
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.63
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.48
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.96
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.37
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 130                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 132                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.68
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.55
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17549.72
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.93
 p-value of test no 146                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.92
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.89
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.96
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.96
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.62
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.89
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.27
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.07
 p-value of test no 157                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.94
 p-value of test no 158                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.77
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.02
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.77
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.06
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.09
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  111.30
 p-value of test no 164                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.72
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  441.57
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.88
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.16
 p-value of test no 168                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.70
 p-value of test no 169                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.60
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.59
 p-value of test no 171                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.68
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.18
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.69
 p-value of test no 174                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.38
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.46
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.04
 p-value of test no 177                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.03
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.63
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 187                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.15
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.64
 p-value of test no 198                :    0.9900
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 200                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.54
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  237.42
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10233.00
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 214                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9842.12
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 216                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 221                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5070.38
 p-value of test no 222                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 223                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.45
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 225                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.08
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4192.82
 p-value of test no 227                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.18
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11584.39
 p-value of test no 229                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.71
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.74
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000007639
 
 Normal statistic for number of bits   :   0.060
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.49
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000052675
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 247                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 248                :    0.81
 
 Sample variance                       :    1.04
 p-value of test no 249                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 253                :    0.96
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:35.85
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35821
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 3                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1462
 p-value of test no 11                 :  4.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334582
   j =  1                              :        599997076
   j =  2                              :             1462
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5494
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7442
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4476
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 24                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 35                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 38                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.05
 p-value of test no 40                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.76
 p-value of test no 42                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.61
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.15
 p-value of test no 47                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.45
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.63
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.19
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.09
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.69
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.36
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  268.13
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.29
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1335.40
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7137.38
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.20
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.45
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.72
 p-value of test no 66                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  120.35
 p-value of test no 67                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4979.75
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45817
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869817
   j =  1                              :        399908373
   j =  2                              :            45803
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45689
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908627
   j =  2                              :            45679
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 73                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 85                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 91                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.68e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
 p-value of test no 112                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.034
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.37e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.35
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.91
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.18
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.02
 p-value of test no 122                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.64
 p-value of test no 123                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.16
 p-value of test no 124                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.73
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.23
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 131                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 132                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.94
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.15
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.49
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 138                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.59
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17287.27
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.93
 p-value of test no 146                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.20
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.74
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   40.16
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.09
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.79
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.86
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.36
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.02
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.53
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.76
 p-value of test no 159                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.61
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.56
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.88
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.67
 p-value of test no 163                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.59
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.84
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.01
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.24
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.63
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.46
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.31
 p-value of test no 170                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.72
 p-value of test no 171                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.98
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.84
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.30
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.55
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.92
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.24
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  4.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 182                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 183                :    0.9903
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 200                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.33
 p-value of test no 203                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 204                :    0.9999    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 206                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.06
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.11
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9935.77
 p-value of test no 215                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 217                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 218                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.57
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.77
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.90
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.68
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11780.90
 p-value of test no 229                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.65
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.44
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000045019
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.00
 p-value of test no 233                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999931967
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.78
 p-value of test no 239                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.064
 p-value of test no 243                :    0.53
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 246                :    0.80
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 247                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    0.68
 p-value of test no 249                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:43:53.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35822
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 7                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7485
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4251
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 18                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     601
 p-value of test no 31                 :    0.49
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 33                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 35                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.80
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.57
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.33
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.70
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.54
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.10
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 52                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.97
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.08
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.58
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.26
 p-value of test no 56                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.74
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.48
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.21
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.59
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.54
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5138.58
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45506
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869506
   j =  1                              :        399908994
   j =  2                              :            45494
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45569
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869569
   j =  1                              :        399908862
   j =  2                              :            45569
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 72                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
 p-value of test no 86                 :    0.9952
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 109                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 114                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.098
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.38
 p-value of test no 119                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.22
 p-value of test no 120                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.86
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.76
 p-value of test no 122                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.36
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.14
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.48
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.70
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.03
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.65
 p-value of test no 135                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.76
 p-value of test no 136                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 138                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 140                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.39
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17097.96
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.96
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.04
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.94
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.59
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.07
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.89
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.17
 p-value of test no 153                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.97
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.40
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.44
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.03
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.31
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.16
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.33
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.30
 p-value of test no 161                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.37
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.95
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.51
 p-value of test no 164                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.84
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.95
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.35
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.86
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.43
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.12
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.27
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.84
 p-value of test no 172                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4976.32
 p-value of test no 173                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.35
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.35
 p-value of test no 175                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.99
 p-value of test no 176                :    0.96
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.69
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.80
 p-value of test no 179                :    0.9974
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 183                :    0.61
 
 Sample variance                       :    2.30
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.52
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
 p-value of test no 190                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
 p-value of test no 191                :    0.66
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
 p-value of test no 193                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 195                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.87
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.46
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.12
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.67
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.71
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10144.26
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 217                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4820.23
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.85
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.63
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.47
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.64
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11561.67
 p-value of test no 230                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.40
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999875648
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   72.27
 p-value of test no 233                :    0.05
 
 
 -----------------------------------------------
 Total number of bits:  7999972800
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 237                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 238                :    0.29
 
 Sample variance                       :    2.02
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 243                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 248                :    0.39
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 250                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.08
 p-value of test no 253                :    0.02
 
 Sample variance                       :    1.54
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:05.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35823
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 8                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 12                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4433
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 16                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4317
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 18                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.82
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 26                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     648
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.65
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 36                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.51
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.73
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.14
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.52
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.78
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.34
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.11
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  404.09
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1355.45
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6911.96
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 59                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.54
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 63                 :  7.2e-3
 
 Anderson-Darling statistic = A2       :    3.48
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   85.02
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.06
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.98
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.54
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908503
   j =  2                              :            45741
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45619
 p-value of test no 71                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869619
   j =  1                              :        399908768
   j =  2                              :            45607
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 91                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.42
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 108                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
 p-value of test no 112                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 9.47e-5
 p-value of test no 113                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.067
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 116                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.03
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.10
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.46
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.86
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.10
 p-value of test no 124                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.02
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 126                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.28
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 131                :    0.22
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 132                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.62
 p-value of test no 133                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 137                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.41
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.88
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.10
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.86
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.76
 p-value of test no 148                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.73
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.21
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.66
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.49
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.70
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.66
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.29
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.24
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.43
 p-value of test no 157                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.64
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.59
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.54
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.53
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.50
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.41
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.68
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.41
 p-value of test no 165                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.26
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.99
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5046.82
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  354.11
 p-value of test no 169                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.34
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.72
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.01
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.77
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.37
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.83
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.13
 p-value of test no 176                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.51
 p-value of test no 178                :    0.9907
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.45
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.18
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.19
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 201                :    0.98
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.33
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 205                :    0.93
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.11
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.86
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.03
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 221                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.66
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.09
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3984.64
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4121.53
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11609.00
 p-value of test no 229                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.61
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.49
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999918587
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.08
 p-value of test no 233                :    0.33
 
 
 -----------------------------------------------
 Total number of bits:  8000051715
 
 Normal statistic for number of bits   :    0.41
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.60
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 238                :    0.63
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.075
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.53
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.36
 p-value of test no 254                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35824
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 8                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 14                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7209
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.14
 p-value of test no 23                 :  7.6e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    3.89
 p-value of test no 26                 :  9.9e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 29                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.41
 p-value of test no 34                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.17
 p-value of test no 47                 :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 48                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.15
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.01
 p-value of test no 50                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.88
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.15
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.46
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.40
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.70
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.76
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6878.59
 p-value of test no 57                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.39
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   79.89
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.74
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.36
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5164.41
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45469
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869469
   j =  1                              :        399909065
   j =  2                              :            45463
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45933
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869933
   j =  1                              :        399908135
   j =  2                              :            45931
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
 p-value of test no 110                :    0.35
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 115                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.051
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -9.67e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.51
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.90
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.51
 p-value of test no 123                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.22
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.13
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.56
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.17
 p-value of test no 135                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 137                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.57
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17536.06
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.63
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.39
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.39
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.16
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.28
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.05
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.39
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.55
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.51
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.58
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.17
 p-value of test no 156                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.88
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.11
 p-value of test no 158                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.71
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.37
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.20
 p-value of test no 161                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.97
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.58
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.88
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.48
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.47
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.91
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.28
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.13
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.15
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.34
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.90
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.75
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.52
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.47
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.34
 p-value of test no 178                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.69
 p-value of test no 179                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 180                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 182                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
 p-value of test no 193                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.98
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.21
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.30
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.51
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.22
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.11
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.28
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.11
 p-value of test no 215                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.82
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.33
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4817.47
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 224                :    0.98
 
 Anderson-Darling statistic = A2       :    4.62
 p-value of test no 225                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4611.77
 p-value of test no 226                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.56
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.30
 p-value of test no 228                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.92
 p-value of test no 229                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.23
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.22
 p-value of test no 231                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  7999979259
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.80
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999911159
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 246                :    0.02
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 248                :    0.02
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:03.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35825
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1455
 p-value of test no 4                  :  7.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334575
   j =  1                              :        599997090
   j =  2                              :             1455
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 5                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 7                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5432
 p-value of test no 13                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 15                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 18                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 19                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7161
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7255
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    1.78
 p-value of test no 26                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 29                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    2.82
 p-value of test no 30                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 32                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.16
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 38                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.94
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 41                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.42
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.53
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.34
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.69
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.67
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.38
 p-value of test no 52                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.15
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  242.62
 p-value of test no 54                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  452.55
 p-value of test no 55                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.35
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.92
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.54
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 62                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.40
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.61
 p-value of test no 66                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.77
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4914.83
 p-value of test no 68                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907804
   j =  2                              :            46092
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46217
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870217
   j =  1                              :        399907572
   j =  2                              :            46205
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 77                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 81                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 92                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 93                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 95                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 99                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
 p-value of test no 109                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 9.71e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 118                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.59
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.76
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.59
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.60
 p-value of test no 122                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.66
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.53
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.82
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.50
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.59
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.16
 p-value of test no 136                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.81
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17576.38
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.02
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.61
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.14
 p-value of test no 148                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.18
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.59
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.45
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.06
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.20
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.57
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.36
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.18
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.94
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.13
 p-value of test no 159                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.79
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.78
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.85
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.09
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.68
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.11
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.05
 p-value of test no 166                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.57
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.44
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.63
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.10
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 171                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.25
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.53
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.52
 p-value of test no 174                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.25
 p-value of test no 175                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.92
 p-value of test no 176                :    0.92
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 177                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.32
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.68
 p-value of test no 179                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.06
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.69
 p-value of test no 198                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 201                :    0.95
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.12
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 204                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.08
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.63
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.93
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9913.38
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.015
 p-value of test no 216                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 219                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4987.14
 p-value of test no 222                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5002.74
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4042.07
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.73
 p-value of test no 228                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.14
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.84
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.75
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000045679
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.85
 p-value of test no 233                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000047827
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.29
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 243                :    0.87
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 247                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 253                :    0.19
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35826
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 3                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 10                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 11                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5350
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 15                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 16                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 21                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 26                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.04
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.30
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     568
 p-value of test no 31                 :    0.90
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 40                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 45                 :    0.9921
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.60
 p-value of test no 46                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.15
 p-value of test no 47                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.34
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.25
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.20
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.54
 p-value of test no 51                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.52
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.03
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.57
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.62
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7083.25
 p-value of test no 57                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.89
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.74
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.11
 p-value of test no 66                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.98
 p-value of test no 67                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.32
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46303
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870303
   j =  1                              :        399907398
   j =  2                              :            46295
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45539
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869539
   j =  1                              :        399908924
   j =  2                              :            45535
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 73                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 105                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 112                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.09
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.99
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.02
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.09
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.34
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.32
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.89
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.03
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.12
 p-value of test no 133                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.84
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.27
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.79
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.92
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17442.32
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.75
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.63
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.69
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.75
 p-value of test no 149                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.38
 p-value of test no 150                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.37
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.56
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.29
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.81
 p-value of test no 154                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.14
 p-value of test no 155                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.96
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.44
 p-value of test no 157                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.58
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.73
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.22
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.41
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.24
 p-value of test no 162                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  441.09
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.30
 p-value of test no 164                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.18
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.10
 p-value of test no 166                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.99
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4885.76
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.50
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.23
 p-value of test no 170                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.71
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.08
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.11
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.27
 p-value of test no 174                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.99
 p-value of test no 175                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.88
 p-value of test no 176                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.35
 p-value of test no 177                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.17
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.71
 p-value of test no 183                :    0.96
 
 Sample variance                       :    0.79
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 187                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 188                :    0.82
 
 Sample variance                       :    1.76
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.31
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.01
 p-value of test no 196                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.40
 p-value of test no 198                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.63
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 206                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.69
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10201.71
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.29
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.085
 p-value of test no 217                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.81
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 223                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.06
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 225                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4999.96
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.58
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.36
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11955.05
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.20
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.86
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999949562
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.12
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000022894
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.85
 p-value of test no 238                :    0.80
 
 Sample variance                       :    1.80
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:05.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35827
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 6                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 9                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 10                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 14                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7385
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7559
 p-value of test no 19                 :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     933
 p-value of test no 25                 :    0.14
 
 Stat. AD (mNP2)                       :    1.71
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 27                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.90
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 44                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.66
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.11
 p-value of test no 48                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.29
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.95
 p-value of test no 50                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.06
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.55
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.25
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  457.82
 p-value of test no 55                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1451.40
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6947.84
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.72
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 62                 :  7.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    3.87
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   33.92
 p-value of test no 65                 :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.64
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.72
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4972.13
 p-value of test no 68                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908097
   j =  2                              :            45944
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46236
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870236
   j =  1                              :        399907530
   j =  2                              :            46232
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 73                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 79                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 84                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 85                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 86                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 88                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 101                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 110                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.41
 p-value of test no 116                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -7.90e-3
 p-value of test no 118                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.43
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.62
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.61
 p-value of test no 122                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.38
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   43.76
 p-value of test no 125                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.36
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 132                :    0.9944
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.21
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.61
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.83
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.22
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.73
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 144                :    0.9977
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17391.97
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.05
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.02
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.58
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.83
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.29
 p-value of test no 150                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.57
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.61
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.58
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.19
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.25
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.69
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.79
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.32
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.80
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.13
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.28
 p-value of test no 162                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.68
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.34
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.26
 p-value of test no 165                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.32
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.31
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4997.04
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.61
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.88
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.29
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.41
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.55
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.35
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.71
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.10
 p-value of test no 176                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.51
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.46
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 182                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 192                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 193                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.99
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.72
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.18
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 206                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.26
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10063.88
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 213                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10307.35
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.068
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 217                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 218                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.10
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.58
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4051.19
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4208.99
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.64
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.31
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.14
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999822617
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.83
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999992084
 
 Normal statistic for number of bits   :  -0.063
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 237                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.26
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 245                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.52
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 253                :    0.50
 
 Sample variance                       :    1.53
 p-value of test no 254                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35828
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 6                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 12                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5513
 p-value of test no 13                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7284
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9907
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.30
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 30                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.23
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.08
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.70
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.91
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.59
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.52
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.79
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.81
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.12
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  505.15
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.67
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7081.67
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.08
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.17
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.46
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.03
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.42
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908311
   j =  2                              :            45843
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907762
   j =  2                              :            46110
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 74                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 80                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 85                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.81e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.09e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.45
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.59
 p-value of test no 120                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.07
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.28
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.62
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.45
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.70
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.86
 p-value of test no 129                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.30
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.68
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.39
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.67
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17395.00
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.03
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.59
 p-value of test no 147                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.89
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.94
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.28
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.57
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.58
 p-value of test no 152                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.82
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.45
 p-value of test no 154                :  6.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.49
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.12
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.48
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.68
 p-value of test no 159                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.93
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.82
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  504.30
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.27
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.08
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.30
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.33
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.70
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.35
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.48
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  444.55
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.77
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.07
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.36
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.39
 p-value of test no 177                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.66
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.76
 p-value of test no 184                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.38
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.23
 p-value of test no 198                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.36
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.87
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10073.98
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.61
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 216                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    3.12
 p-value of test no 217                :  9.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.49
 p-value of test no 218                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 221                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4928.09
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 224                :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.98
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.02
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.46
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.63
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.71
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.38
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  7999840551
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.47
 p-value of test no 233                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000044317
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 236                :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    1.83
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:58.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  93  HammingCorr, L = 300            9.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35829
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 3                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 4                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 7                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 11                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5338
 p-value of test no 13                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 14                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 19                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 26                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.99
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.26
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     291
 p-value of test no 37                 :    0.69
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 40                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.12
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.08
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.40
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.00
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.11
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.76
 p-value of test no 51                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.03
 p-value of test no 52                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  185.04
 p-value of test no 54                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.60
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.92
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.89
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.95
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.05
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.04
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.16
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4947.57
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45566
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869566
   j =  1                              :        399908878
   j =  2                              :            45546
   j =  3                              :               10
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46176
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870176
   j =  1                              :        399907654
   j =  2                              :            46164
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 84                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 91                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 104                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
 p-value of test no 109                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 111                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 116                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.37
 p-value of test no 117                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.58
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.24
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.06
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.88
 p-value of test no 121                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.96
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.37
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.87
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   54.13
 p-value of test no 125                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.67
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.05
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.99
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.81
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.94
 p-value of test no 136                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.53
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 143                :    0.10
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17606.74
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.44
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.78
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.52
 p-value of test no 148                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.59
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.64
 p-value of test no 151                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.86
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.00
 p-value of test no 153                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.13
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.53
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.44
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  550.18
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  109.43
 p-value of test no 159                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.17
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.39
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.84
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.70
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.16
 p-value of test no 164                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.20
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.98
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  445.85
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.14
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  350.35
 p-value of test no 169                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.36
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.02
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.95
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4947.74
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.33
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.47
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.51
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 181                :    0.02
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.47
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.36
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.67
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.18e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
 p-value of test no 194                :    0.87
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.26
 p-value of test no 196                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.85
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  233.09
 p-value of test no 203                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.40
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.70
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.95
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9838.77
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.84
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.20
 p-value of test no 222                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5012.63
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.16
 p-value of test no 227                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.47
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11914.73
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11719.11
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.91
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  7999966950
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.10
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999957029
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 236                :    0.86
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.34
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 245                :  7.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 246                :    0.85
 
 Anderson-Darling statistic = A2       :    2.70
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.62
 p-value of test no 248                :    0.95
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35830
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 9                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1280
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334400
   j =  1                              :        599997440
   j =  2                              :             1280
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4297
 p-value of test no 14                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 21                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    7.95
 p-value of test no 27                 :  1.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 38                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     171
 p-value of test no 43                 :    0.05
 
 Stat. AD (mNP2)                       :    1.25
 p-value of test no 44                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.70
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.96
 p-value of test no 47                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.10
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.55
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.05
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.04
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.07
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.90
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.72
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.24
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.81
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.62
 p-value of test no 59                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.69
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.99
 p-value of test no 61                 :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.25
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.84
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.42
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.12
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45798
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869798
   j =  1                              :        399908410
   j =  2                              :            45786
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 71                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907653
   j =  2                              :            46163
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 77                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 78                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 103                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.05
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 105                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 107                :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 114                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.85
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 117                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.76
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.65
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.33
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.33
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.40
 p-value of test no 123                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.31
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.37
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.22
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 132                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.81
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.76
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.16
 p-value of test no 141                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17563.87
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.25
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.28
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.72
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    8.76
 p-value of test no 149                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.50
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.55
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.17
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.61
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.09
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.99
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.83
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.57
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  574.88
 p-value of test no 158                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.55
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.38
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.58
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.09
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.01
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.72
 p-value of test no 165                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.02
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.99
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.61
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.45
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.30
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.18
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.93
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5044.86
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.28
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.64
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.69
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.35
 p-value of test no 178                :    0.42
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 182                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
 p-value of test no 193                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.38
 p-value of test no 196                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.19
 p-value of test no 198                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.10
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.50
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.27
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.25
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.46
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.074
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.28
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 221                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.38
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.25
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.88
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4140.18
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.46
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11636.09
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12005.81
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.55
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999867095
 
 Normal statistic for number of bits   :   -1.05
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.70
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999971372
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 236                :    0.94
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 237                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 243                :    0.18
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 248                :    0.33
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:24.56
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP2S, t = 3         1.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35831
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 9                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 17                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 22                 :    0.9960
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.05
 p-value of test no 32                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.15
 p-value of test no 34                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 35                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    2.17
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 45                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.30
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.33
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.49
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.39
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.30
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.98
 p-value of test no 51                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.57
 p-value of test no 52                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.66
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.30
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.93
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1500.08
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7195.88
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.83
 p-value of test no 65                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.04
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.02
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5128.04
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45703
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869703
   j =  1                              :        399908595
   j =  2                              :            45701
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908688
   j =  2                              :            45647
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 87                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 91                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 100                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
 p-value of test no 109                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.17
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.41
 p-value of test no 119                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.74
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.37
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.50
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.19
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.58
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.85
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.97
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.93
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 135                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.82
 p-value of test no 136                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 140                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.06
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 143                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17330.68
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.51
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.92
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.52
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.06
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.42
 p-value of test no 152                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.40
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.73
 p-value of test no 154                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.30
 p-value of test no 156                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.49
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.26
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.53
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  101.85
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.80
 p-value of test no 161                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.79
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.85
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.90
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.85
 p-value of test no 165                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.90
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.40
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4903.66
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.64
 p-value of test no 169                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.86
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.81
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.29
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4913.80
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  438.77
 p-value of test no 174                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.05
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.90
 p-value of test no 176                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.47
 p-value of test no 177                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.94
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.17
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 181                :    0.85
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.81
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.07
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.50
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.20
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.21
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.96
 p-value of test no 211                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.58
 p-value of test no 215                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.99
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4862.55
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5026.25
 p-value of test no 226                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.37
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4089.61
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.88
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11653.54
 p-value of test no 230                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.93
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999885290
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.51
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999957479
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.052
 p-value of test no 238                :    0.48
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.081
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.19
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35832
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1453
 p-value of test no 4                  :  8.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334573
   j =  1                              :        599997094
   j =  2                              :             1453
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 7                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 11                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5346
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 17                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7439
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 24                 :    0.9956
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.47
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.45
 p-value of test no 46                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.39
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.73
 p-value of test no 48                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.82
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.59
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.79
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.93
 p-value of test no 52                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.69
 p-value of test no 53                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.30
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  517.20
 p-value of test no 55                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.25
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6917.91
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.86
 p-value of test no 61                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 64                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.78
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.72
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.01
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.29
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45834
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869834
   j =  1                              :        399908334
   j =  2                              :            45830
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45947
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869947
   j =  1                              :        399908110
   j =  2                              :            45939
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 80                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 84                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 85                 :    0.9920
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 92                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 93                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 95                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 97                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 98                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 101                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
 p-value of test no 109                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
 p-value of test no 110                :    0.79
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 115                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 116                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.060
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 118                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.99
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.28
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.44
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.63
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.99
 p-value of test no 123                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.76
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.77
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 126                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.28
 p-value of test no 129                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 130                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.86
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 140                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.24
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17495.49
 p-value of test no 145                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.68
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.72
 p-value of test no 147                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.93
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.69
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.75
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.39
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.45
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.54
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.95
 p-value of test no 154                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.72
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.04
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.19
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.99
 p-value of test no 158                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.34
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.75
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.05
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.88
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.99
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.67
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.85
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.56
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.00
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.07
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.98
 p-value of test no 170                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.08
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.40
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.52
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.75
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.92
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.11
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 178                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.11
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 181                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 183                :    0.13
 
 Sample variance                       :    0.17
 p-value of test no 184                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
 p-value of test no 190                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 191                :    0.48
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.97
 p-value of test no 196                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.53
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.70
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 205                :    0.06
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  225.94
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9921.18
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9952.35
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.42
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 217                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 220                :    0.89
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.06
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.56
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4050.40
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4093.07
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11827.42
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.52
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.99
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000122329
 
 Normal statistic for number of bits   :    0.97
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.02
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999932480
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 236                :  6.2e-3
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.99
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 243                :    0.23
 
 Sample variance                       :    0.98
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 245                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.36
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 253                :    0.62
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:24.82
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35833
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 5                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 7                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5457
 p-value of test no 13                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7474
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 18                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7228
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     927
 p-value of test no 25                 :    0.19
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     628
 p-value of test no 31                 :    0.13
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 33                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.82
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.88
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.26
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.48
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 51                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.42
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.63
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.20
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.57
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.95
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.07
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.59
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    3.21
 p-value of test no 64                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   90.86
 p-value of test no 65                 :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.86
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.12
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4941.36
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45636
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869636
   j =  1                              :        399908736
   j =  2                              :            45620
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908143
   j =  2                              :            45921
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 72                 :  3.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.14
 p-value of test no 74                 :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9951
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 77                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.23
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 85                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
 p-value of test no 90                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 99                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 100                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 103                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 105                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 116                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.29
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.36
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.12
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.26
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.42
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.01
 p-value of test no 125                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 127                :  6.9e-3
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.39
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.87
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.05
 p-value of test no 134                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.52
 p-value of test no 135                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 136                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  159.43
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17359.22
 p-value of test no 145                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.90
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.62
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.99
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.48
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.38
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.59
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.39
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.82
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.79
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.45
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.47
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.99
 p-value of test no 157                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.12
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.26
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.91
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.54
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.85
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.46
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.90
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.17
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.07
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.24
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5064.31
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  280.12
 p-value of test no 169                : 1 -  4.8e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.72
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.99
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.42
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.12
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.92
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.80
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.85
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.73
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.91
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.82
 p-value of test no 189                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 191                :    0.71
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.86
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.06
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.39
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.21
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.15
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 212                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 214                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9833.51
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.95
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.64
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.48
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.43
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.17
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12083.22
 p-value of test no 229                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.51
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000039307
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.85
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000171697
 
 Normal statistic for number of bits   :    1.36
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 237                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 238                :    0.31
 
 Sample variance                       :    1.50
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 240                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.86
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 246                :    0.82
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 248                :    0.73
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 252                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 253                :    0.21
 
 Sample variance                       :    1.58
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:20.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  78  RandomWalk1 R (L=10000, r=0)   1 -  4.8e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35834
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 5                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 7                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 10                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 12                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5507
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 14                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4460
 p-value of test no 16                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 23                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 35                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 42                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    2.68
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.58
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.63
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.48
 p-value of test no 48                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.80
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.57
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.38
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.27
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.24
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  481.11
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1480.97
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7281.75
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.75
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 64                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   81.15
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.66
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.44
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908332
   j =  2                              :            45828
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908534
   j =  2                              :            45727
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 74                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 90                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.56
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
 p-value of test no 110                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 115                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.79
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 118                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.57
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.62
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.88
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.61
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.60
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.82
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.90
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.22
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.32
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.86
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.82
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.06
 p-value of test no 135                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 140                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.37
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 144                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17100.68
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.75
 p-value of test no 146                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.56
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.94
 p-value of test no 148                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.57
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.58
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.20
 p-value of test no 151                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.24
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.51
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.88
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.11
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.72
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.95
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.36
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.37
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.47
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.38
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.30
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.52
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.36
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.00
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.91
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.28
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.52
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.47
 p-value of test no 169                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.73
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.65
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.73
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.88
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.18
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.17
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.80
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.51
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.49
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
 p-value of test no 186                :    0.9929
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.14
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.26
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.63
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 200                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  244.39
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.52
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.83
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9910.32
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.52
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.94
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.43
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.74
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11637.91
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12017.79
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.58
 p-value of test no 231                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  7999924197
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.16
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  7999978638
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.68
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.38
 p-value of test no 249                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.32
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:54.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35835
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 3                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 5                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5275
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 14                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7427
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 19                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 21                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.62
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    3.20
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     960
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     636
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.85
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.52
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.59
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.51
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.81
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.00
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.38
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.16
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.96
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.13
 p-value of test no 52                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.18
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  232.82
 p-value of test no 54                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  413.95
 p-value of test no 55                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1510.70
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6937.06
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.33
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.42
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   0.076
 p-value of test no 66                 : 1 -  8.2e-5    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.57
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4993.07
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45845
 p-value of test no 70                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869845
   j =  1                              :        399908316
   j =  2                              :            45833
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908927
   j =  2                              :            45532
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 78                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.10e-4
 p-value of test no 104                :    0.9993    *****
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 118                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.00
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.57
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.06
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.68
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.73
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.49
 p-value of test no 124                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.53
 p-value of test no 125                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 128                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.87
 p-value of test no 129                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.18
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.13
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.76
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.66
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.00
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.50
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.64
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.51
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.33
 p-value of test no 149                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.59
 p-value of test no 150                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.42
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.26
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.05
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.78
 p-value of test no 154                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.66
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.83
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.48
 p-value of test no 157                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.05
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.40
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.66
 p-value of test no 160                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.78
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.05
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.44
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.32
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.38
 p-value of test no 165                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.68
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.50
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5107.07
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.81
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.79
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.34
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.09
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.88
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.76
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.49
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.07
 p-value of test no 178                :    0.36
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 181                :    0.98
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 183                :    0.99
 
 Sample variance                       :    0.61
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 187                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.22
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
 p-value of test no 194                :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.29
 p-value of test no 196                :    0.51
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.86
 p-value of test no 198                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 202                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.08
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.84
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 209                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9973.53
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10282.17
 p-value of test no 215                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.070
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.19
 p-value of test no 218                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.39
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.27
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3991.71
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3964.87
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11967.11
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.63
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.81
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999860789
 
 Normal statistic for number of bits   :   -1.10
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.51
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000036463
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.74
 p-value of test no 239                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 243                :    0.05
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 248                :    0.89
 
 Sample variance                       :    0.66
 p-value of test no 249                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.83
 p-value of test no 254                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:09.27
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3             1 -  8.2e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35836
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 3                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 5                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5371
 p-value of test no 13                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 14                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 23                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    1.54
 p-value of test no 26                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 30                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    3.27
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.92
 p-value of test no 45                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.89
 p-value of test no 46                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.99
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.49
 p-value of test no 48                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.17
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.03
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.94
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.18
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  451.02
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.60
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6997.34
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 60                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.38
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.07
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.40
 p-value of test no 67                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.51
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45905
 p-value of test no 70                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869905
   j =  1                              :        399908193
   j =  2                              :            45899
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45599
 p-value of test no 71                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869599
   j =  1                              :        399908805
   j =  2                              :            45593
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 74                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 80                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 81                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
 p-value of test no 83                 :    0.9997    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 98                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.27
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 103                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 110                :    0.47
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.12
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 116                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.094
 p-value of test no 117                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.16
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.21
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.60
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.08
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.92
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.81
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.50
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.01
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.17
 p-value of test no 134                :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.78
 p-value of test no 136                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.36
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17690.81
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.29
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.58
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.58
 p-value of test no 148                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.24
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.60
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.33
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.37
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.11
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.36
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.07
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.41
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.01
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.51
 p-value of test no 158                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.98
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.14
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.74
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.30
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.99
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.07
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.97
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.07
 p-value of test no 166                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.76
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.85
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.39
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.65
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.65
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.00
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.63
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.40
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.02
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.37
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.12
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.22
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 179                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 182                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.016
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.77
 p-value of test no 198                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.91
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.69
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10101.84
 p-value of test no 211                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.41
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.05
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  9.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 220                :    0.95
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 221                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4683.51
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4964.59
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.51
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.11
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11814.83
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11791.39
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000042106
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.63
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999979094
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 234                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 237                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.087
 p-value of test no 238                :    0.53
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 241                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.62
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 246                :    0.83
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 248                :    0.95
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    2.86
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.23
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:09.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35837
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 9                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4425
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.15
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.67
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     954
 p-value of test no 25                 :    0.04
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     621
 p-value of test no 31                 :    0.20
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 33                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.34
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.50
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.10
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.29
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.54
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.72
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.44
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.32
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.24
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.09
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1377.13
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.04
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   43.90
 p-value of test no 61                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.69
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.37
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.16
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5003.10
 p-value of test no 68                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 70                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908396
   j =  2                              :            45799
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45632
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869632
   j =  1                              :        399908743
   j =  2                              :            45618
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 74                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 79                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 95                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 102                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 104                :    0.03
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 105                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 107                :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 108                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
 p-value of test no 110                :    0.85
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
 p-value of test no 113                :    0.61
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 114                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.097
 p-value of test no 116                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.38
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.10
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.03
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.72
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.37
 p-value of test no 124                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.87
 p-value of test no 125                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.56
 p-value of test no 126                :  8.8e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 127                :    0.93
 
 Anderson-Darling statistic = A2       :    4.24
 p-value of test no 128                :  7.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   19.06
 p-value of test no 129                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 132                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.63
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.30
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.01
 p-value of test no 136                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.21
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.68
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 144                :    0.9997    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17477.59
 p-value of test no 145                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.89
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.37
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.15
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.59
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 150                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.30
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.31
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.87
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.93
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.80
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.18
 p-value of test no 156                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.85
 p-value of test no 157                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.86
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.16
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.39
 p-value of test no 160                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.33
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.07
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.40
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.18
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.83
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  470.98
 p-value of test no 166                :  1.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  448.42
 p-value of test no 167                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5136.58
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  416.77
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.63
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.58
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.77
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.92
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.39
 p-value of test no 174                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.25
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.72
 p-value of test no 176                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.14
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 180                :  5.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 182                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.84
 p-value of test no 183                :    0.97
 
 Sample variance                       :    0.22
 p-value of test no 184                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.95
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.69
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.06
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 205                :    0.78
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.43
 p-value of test no 207                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 210                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.44
 p-value of test no 211                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 212                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10118.61
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : 4.52e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.06
 p-value of test no 217                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 218                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.66
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4954.22
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.66
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3937.00
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.95
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11856.96
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.68
 p-value of test no 231                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000032971
 
 Normal statistic for number of bits   :    0.26
 p-value of test no 232                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.83
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999868274
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 243                :    0.67
 
 Sample variance                       :    2.08
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.97
 p-value of test no 249                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.55
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:16.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35838
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 3                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 4                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 12                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5437
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 19                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.63
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 26                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    1.45
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.33
 p-value of test no 28                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 33                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.40
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.00
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.48
 p-value of test no 46                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.96
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.86
 p-value of test no 48                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.85
 p-value of test no 49                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.78
 p-value of test no 50                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.26
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.08
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.31
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.07
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.26
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.13
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6967.11
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.12
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.80
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.26
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.11
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.61
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45441
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869441
   j =  1                              :        399909119
   j =  2                              :            45439
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46137
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870137
   j =  1                              :        399907730
   j =  2                              :            46129
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 73                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 79                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 81                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 104                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
 p-value of test no 109                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 3.30e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 111                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 115                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.059
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.91
 p-value of test no 120                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.04
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.70
 p-value of test no 122                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.64
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.47
 p-value of test no 124                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.61
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.50
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.96
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.23
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 137                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    3.53
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  172.22
 p-value of test no 141                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17615.27
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.47
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.49
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.03
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.36
 p-value of test no 149                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.75
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.55
 p-value of test no 151                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.31
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.79
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.97
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.84
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.98
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.38
 p-value of test no 157                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.42
 p-value of test no 158                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.12
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.51
 p-value of test no 161                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.80
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.28
 p-value of test no 163                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.26
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.55
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.47
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.53
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4868.33
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  321.56
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.23
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  309.06
 p-value of test no 171                :    0.9980
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.39
 p-value of test no 172                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.08
 p-value of test no 173                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.42
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.02
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.94
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.17
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.19
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9948
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.26
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.35
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.47
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.81
 p-value of test no 203                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 206                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.50
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.84
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10029.85
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 217                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 218                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.96
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.49
 p-value of test no 226                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.67
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4197.75
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.33
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.15
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.85
 p-value of test no 231                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  8000015073
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.06
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000030970
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.76
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.71
 p-value of test no 249                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 251                :    0.20
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 252                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.45
 p-value of test no 253                :    0.07
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:45.22
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35839
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 8                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 10                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5470
 p-value of test no 13                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 21                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 24                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.74
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    2.38
 p-value of test no 38                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 40                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     134
 p-value of test no 43                 :    0.90
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.20
 p-value of test no 45                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.13
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.83
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.66
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.93
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.88
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.63
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.43
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.98
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  387.84
 p-value of test no 55                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1459.80
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7068.26
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 60                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.48
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.15
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.15
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.39
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5086.61
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 70                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908197
   j =  2                              :            45900
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908403
   j =  2                              :            45794
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 94                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 108                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 111                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.30
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.24
 p-value of test no 120                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.20
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.36
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.45
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.76
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.88
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.85
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   13.06
 p-value of test no 135                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 137                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.23
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.92
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17143.79
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.07
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   63.10
 p-value of test no 147                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.28
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.61
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.33
 p-value of test no 150                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.66
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.36
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.90
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.23
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.73
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.54
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.99
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.28
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.06
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.32
 p-value of test no 160                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.63
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.63
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.28
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.91
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.01
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.19
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.99
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.03
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.46
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.11
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.20
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.66
 p-value of test no 172                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4869.13
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.69
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.56
 p-value of test no 175                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.62
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.11
 p-value of test no 177                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.87
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 181                :    0.84
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 187                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.79
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 192                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
 p-value of test no 193                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.25
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.60
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.02
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.46
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 208                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 209                :    0.05
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 210                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10195.60
 p-value of test no 211                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 212                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10326.37
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.88
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 224                :    0.83
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4778.23
 p-value of test no 226                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.98
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.12
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.79
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12066.44
 p-value of test no 230                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.06
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999884708
 
 Normal statistic for number of bits   :   -0.91
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.54
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999875813
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 238                :    0.90
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 245                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 247                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:55.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35840
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 7                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1262
 p-value of test no 9                  :    0.9973
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334382
   j =  1                              :        599997476
   j =  2                              :             1262
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 11                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 12                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4196
 p-value of test no 14                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 15                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 16                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.56
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 24                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     899
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 26                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.15
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.19
 p-value of test no 34                 :    0.9925
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.37
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.68
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.59
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.79
 p-value of test no 48                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.89
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.11
 p-value of test no 51                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.83
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.93
 p-value of test no 53                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.82
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.22
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1600.87
 p-value of test no 56                 :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.85
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.64
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.92
 p-value of test no 65                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.10
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.42
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.80
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45985
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869985
   j =  1                              :        399908033
   j =  2                              :            45979
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45537
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869537
   j =  1                              :        399908930
   j =  2                              :            45529
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 72                 :    0.9936
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.94
 p-value of test no 74                 :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  2.2e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 83                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 102                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 111                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
 p-value of test no 113                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.45
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.73
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.03
 p-value of test no 121                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.53
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.00
 p-value of test no 123                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.51
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.09
 p-value of test no 125                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.66
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.27
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.18
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.68
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.01
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.63
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.63
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.58
 p-value of test no 146                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.13
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.36
 p-value of test no 148                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.80
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.88
 p-value of test no 151                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.25
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.93
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.40
 p-value of test no 154                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.47
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.66
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  193.78
 p-value of test no 157                :  5.0e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.86
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.68
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.69
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.37
 p-value of test no 161                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.22
 p-value of test no 162                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.73
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.96
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.05
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.61
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.09
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.36
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.50
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.12
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.74
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.19
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.10
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.72
 p-value of test no 174                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.74
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.62
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.00
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.25
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.54
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 187                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.38
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.06
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.04
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.54
 p-value of test no 207                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10145.45
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 214                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9893.05
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.18
 p-value of test no 222                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.95
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4012.27
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.73
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12042.42
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.43
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.49
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999933788
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.73
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999807725
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 238                :    0.10
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 241                :    0.92
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 243                :    0.81
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 246                :    0.95
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.28
 p-value of test no 248                :    0.90
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.028
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:25.15
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35841
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 6                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 8                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 12                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5270
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 14                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 19                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 21                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 22                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.66
 p-value of test no 26                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 30                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 33                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     310
 p-value of test no 37                 :    0.29
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.24
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.31
 p-value of test no 44                 :    0.93
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.04
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.86
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.97
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.01
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.55
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.14
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.80
 p-value of test no 52                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.28
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.23
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.87
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1494.96
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7113.44
 p-value of test no 57                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.94
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.90
 p-value of test no 65                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.04
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   92.85
 p-value of test no 67                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.57
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 70                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908412
   j =  2                              :            45791
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907953
   j =  2                              :            46013
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 78                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 79                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 93                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 101                :    0.49
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.48
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
 p-value of test no 109                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.35e-5
 p-value of test no 112                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.62
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.27
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.35
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.52
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.91
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.09
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.60
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.41
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.45
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.78
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 140                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.18
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17444.03
 p-value of test no 145                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.51
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.42
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.87
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.30
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.68
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.35
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.58
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.46
 p-value of test no 153                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 154                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.96
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.86
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.90
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.48
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.47
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.99
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.71
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  105.16
 p-value of test no 162                :    0.9956
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.77
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.57
 p-value of test no 164                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.89
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.78
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.89
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5194.12
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.76
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.78
 p-value of test no 170                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.76
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.08
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5122.13
 p-value of test no 173                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  450.86
 p-value of test no 174                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.74
 p-value of test no 175                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.79
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.45
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.93
 p-value of test no 183                :    0.18
 
 Sample variance                       :    0.74
 p-value of test no 184                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 185                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 188                :    0.30
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 192                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.45
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.50
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.63
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.55
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.18
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.65
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4810.75
 p-value of test no 222                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.12
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4182.08
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.76
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11807.48
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11385.16
 p-value of test no 230                :    0.9981
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.10
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  7999981152
 
 Normal statistic for number of bits   :   -0.15
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.40
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999932624
 
 Normal statistic for number of bits   :   -0.53
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.65
 p-value of test no 239                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 240                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.34
 p-value of test no 243                :    0.9904
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 246                :    0.93
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 248                :    0.80
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35842
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5509
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 20                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 22                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    3.25
 p-value of test no 26                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 36                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     329
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 38                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 46                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.77
 p-value of test no 47                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.25
 p-value of test no 48                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.31
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.05
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.15
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.97
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.50
 p-value of test no 53                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.02
 p-value of test no 54                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.76
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1347.94
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.73
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.50
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.91
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.06
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.14
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.03
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907954
   j =  2                              :            46020
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908518
   j =  2                              :            45738
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 74                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  7.7e-3
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 100                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 101                :    0.97
 
 Anderson-Darling statistic = A2       :    4.38
 p-value of test no 102                :  5.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 109                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 111                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 114                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.56
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.46
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.00
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.92
 p-value of test no 122                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.76
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.04
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.35
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 127                :    0.78
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 128                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.76
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 132                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.28
 p-value of test no 133                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.00
 p-value of test no 141                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17806.65
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.54
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.22
 p-value of test no 147                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.37
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.59
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.40
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.96
 p-value of test no 151                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.94
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.58
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.10
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.32
 p-value of test no 156                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.05
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.58
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.97
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.71
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.32
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.15
 p-value of test no 162                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.47
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.52
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.27
 p-value of test no 165                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.50
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.54
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.95
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.63
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.57
 p-value of test no 170                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 171                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.85
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.47
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.92
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.45
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.62
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.58
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.14
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 179                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.97
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.23
 
 Sample variance                       :    0.51
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 190                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.94
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.62
 p-value of test no 203                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 206                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.58
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9946.83
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 212                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 214                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.09
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.93
 p-value of test no 217                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.89
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.35
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.88
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.41
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.15
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11703.29
 p-value of test no 230                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.33
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000198703
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.68
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000042928
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 235                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 238                :    0.76
 
 Sample variance                       :    0.35
 p-value of test no 239                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 242                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 243                :    0.71
 
 Sample variance                       :    2.36
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 245                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 251                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 252                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.74
 p-value of test no 254                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:39.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35843
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 6                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 9                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 10                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5362
 p-value of test no 13                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7530
 p-value of test no 20                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 24                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.86
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 34                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 35                 :    0.9928
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     348
 p-value of test no 37                 :  3.6e-3
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 38                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.27
 p-value of test no 40                 :  7.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.34
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.14
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.28
 p-value of test no 48                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.43
 p-value of test no 49                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.72
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.06
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.31
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.86
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.79
 p-value of test no 54                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.26
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1365.78
 p-value of test no 56                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7059.25
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.17
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.13
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.84
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  153.17
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4798.73
 p-value of test no 68                 :    0.9924
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45820
 p-value of test no 70                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869820
   j =  1                              :        399908365
   j =  2                              :            45810
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45567
 p-value of test no 71                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869567
   j =  1                              :        399908867
   j =  2                              :            45565
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 73                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 80                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 101                :    0.48
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 2.90e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.33
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.62
 p-value of test no 120                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.01
 p-value of test no 121                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.68
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.64
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.05
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.42
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
 p-value of test no 127                :    0.9923
 
 Anderson-Darling statistic = A2       :    3.33
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   20.88
 p-value of test no 129                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.18
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.46
 p-value of test no 134                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.31
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 136                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.71
 p-value of test no 137                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  130.11
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    2.71
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17113.38
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.60
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.75
 p-value of test no 147                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.13
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   38.95
 p-value of test no 149                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.50
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.88
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.89
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.92
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.45
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.20
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.23
 p-value of test no 157                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.32
 p-value of test no 158                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.95
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.52
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.12
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.80
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.24
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.12
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.60
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.63
 p-value of test no 166                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.97
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.78
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.30
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.11
 p-value of test no 170                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.15
 p-value of test no 171                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  323.10
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.78
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.16
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.79
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.61
 p-value of test no 177                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 183                :    0.15
 
 Sample variance                       :    0.86
 p-value of test no 184                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 190                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.41
 p-value of test no 196                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.90
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
 p-value of test no 200                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.38
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 204                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.52
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10211.46
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.47
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.26
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4918.96
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.16
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.53
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.07
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.53
 p-value of test no 228                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11952.53
 p-value of test no 229                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11801.50
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.62
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000105790
 
 Normal statistic for number of bits   :    0.84
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.67
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000019528
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-3
 p-value of test no 236                :    0.9982
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.54
 p-value of test no 238                :    0.9945
 
 Sample variance                       :    1.18
 p-value of test no 239                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 248                :    0.22
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 252                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.47
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:37.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35844
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 3                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 5                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 15                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 24                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 41                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.83
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.33
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.98
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.69
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.73
 p-value of test no 49                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.63
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.17
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.48
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   87.19
 p-value of test no 53                 :  2.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.23
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.84
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.73
 p-value of test no 56                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6999.80
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.02
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.29
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.71
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  157.80
 p-value of test no 67                 :  1.0e-2
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.00
 p-value of test no 68                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45746
 p-value of test no 70                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869746
   j =  1                              :        399908510
   j =  2                              :            45742
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46173
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870173
   j =  1                              :        399907660
   j =  2                              :            46161
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 100                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-3
 p-value of test no 104                :    0.9987
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 112                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.75
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.54
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.30
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.66
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.71
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.09
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.98
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.91
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.35
 p-value of test no 133                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.90
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.56
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 139                :  1.6e-3
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.79
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17168.58
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.58
 p-value of test no 146                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.85
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.64
 p-value of test no 149                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.80
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.28
 p-value of test no 151                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.35
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.20
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.19
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.86
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.03
 p-value of test no 157                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  551.46
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.81
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.07
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.04
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.47
 p-value of test no 162                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  489.88
 p-value of test no 163                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.85
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.42
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.77
 p-value of test no 166                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.73
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.76
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.89
 p-value of test no 169                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.85
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.43
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.78
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4891.93
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.02
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.80
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   24.57
 p-value of test no 176                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.67
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.35
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.31
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.48
 p-value of test no 184                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 188                :    0.47
 
 Sample variance                       :    0.71
 p-value of test no 189                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 192                :    0.9916
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.42e-3
 p-value of test no 194                :    0.91
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.62
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   40.00
 p-value of test no 197                :  4.5e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.76
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.22
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.63
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9897.74
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9905.40
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.084
 p-value of test no 217                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4944.93
 p-value of test no 222                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4977.08
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3976.20
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4235.64
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.62
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.62
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.36
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999933662
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.21
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  7999921464
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.19
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 243                :    0.36
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 247                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.66
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 253                :  6.2e-3
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:38.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35845
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 11                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997255
   j =  2                              :             1371
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5355
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4279
 p-value of test no 14                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 15                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4480
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7500
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 20                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 21                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.88
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     870
 p-value of test no 25                 :    0.84
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 26                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 29                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 30                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    2.82
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 36                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.15
 p-value of test no 39                 :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.96
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.34
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.27
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.47
 p-value of test no 50                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.18
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.06
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.17
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.55
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.95
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7089.60
 p-value of test no 57                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.91
 p-value of test no 61                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.63
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.64
 p-value of test no 67                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.73
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46019
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870019
   j =  1                              :        399907963
   j =  2                              :            46017
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45790
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869790
   j =  1                              :        399908423
   j =  2                              :            45784
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 78                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 88                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.58
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
 p-value of test no 109                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
 p-value of test no 113                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 117                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.39
 p-value of test no 118                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.18
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.75
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.94
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.78
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.97
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.67
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.39
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.72
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.25
 p-value of test no 133                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.34
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    3.15
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   94.96
 p-value of test no 141                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.36
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.48
 p-value of test no 146                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.16
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.74
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.94
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.21
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.92
 p-value of test no 151                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.01
 p-value of test no 152                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.68
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.72
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.99
 p-value of test no 155                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.71
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.68
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.29
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.79
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.33
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.82
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.89
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.01
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.36
 p-value of test no 164                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  105.46
 p-value of test no 165                :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.57
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.35
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.03
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.44
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.42
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.61
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.01
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.76
 p-value of test no 173                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.55
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.09
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.39
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.59
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.069
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 187                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 192                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.18
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.37
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 202                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.34
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.97
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.18
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 212                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 213                :    0.99
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9637.47
 p-value of test no 215                :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.67
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.64
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4775.67
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4703.12
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3965.41
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4124.38
 p-value of test no 228                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11450.47
 p-value of test no 229                :    0.9930
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11607.01
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.14
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  8000066619
 
 Normal statistic for number of bits   :    0.53
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.52
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999961697
 
 Normal statistic for number of bits   :   -0.30
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 242                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.20
 p-value of test no 243                :    0.99
 
 Sample variance                       :    0.71
 p-value of test no 244                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    2.63
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.08
 p-value of test no 248                :    0.86
 
 Sample variance                       :    2.80
 p-value of test no 249                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 250                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 251                :    0.98
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.09
 p-value of test no 253                :    0.98
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35846
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 3                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 12                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 14                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7394
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 16                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 18                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.70
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    1.69
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    3.09
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.43
 p-value of test no 29                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.91
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.95
 p-value of test no 35                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.75
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    1.58
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     174
 p-value of test no 43                 :    0.03
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.64
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.62
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.90
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.59
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.77
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.27
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.64
 p-value of test no 52                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.42
 p-value of test no 53                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.00
 p-value of test no 54                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.12
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1429.01
 p-value of test no 56                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.60
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.45
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.76
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.65
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.11
 p-value of test no 67                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.83
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45867
 p-value of test no 70                 :    0.52
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869867
   j =  1                              :        399908270
   j =  2                              :            45859
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45902
 p-value of test no 71                 :    0.46
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869902
   j =  1                              :        399908197
   j =  2                              :            45900
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 73                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.63
 p-value of test no 85                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.32e-3
 p-value of test no 101                :    0.9935
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 110                :    0.67
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.88e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 118                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.96
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.54
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.97
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.26
 p-value of test no 123                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.84
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.55
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 131                :  5.8e-3
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.03
 p-value of test no 133                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.34
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.94
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.87
 p-value of test no 141                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17318.35
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.34
 p-value of test no 146                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.35
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.44
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.34
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.07
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.20
 p-value of test no 151                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.26
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.08
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.88
 p-value of test no 156                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.84
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.06
 p-value of test no 158                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.80
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.34
 p-value of test no 160                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.68
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.50
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   99.27
 p-value of test no 164                :    0.9923
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.78
 p-value of test no 165                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.07
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.12
 p-value of test no 167                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5166.06
 p-value of test no 168                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.79
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.41
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.34
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.18
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.77
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.29
 p-value of test no 174                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.53
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.22
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.10
 p-value of test no 179                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 183                :    0.31
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 187                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 188                :    0.80
 
 Sample variance                       :    0.98
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 192                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.30
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.24
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 202                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.47
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 205                :    0.91
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  165.44
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10087.50
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10062.52
 p-value of test no 215                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.083
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.059
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.74
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4787.76
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4304.53
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.28
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11887.04
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11659.53
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.28
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999840377
 
 Normal statistic for number of bits   :   -1.26
 p-value of test no 232                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.21
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000058927
 
 Normal statistic for number of bits   :    0.47
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 238                :    0.13
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 240                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 253                :    0.31
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:52.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35847
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 6                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 7                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 11                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5481
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4371
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4413
 p-value of test no 16                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7361
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     939
 p-value of test no 25                 :    0.10
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 29                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    1.22
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    4.41
 p-value of test no 33                 :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 34                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 35                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    2.80
 p-value of test no 36                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    2.83
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 45                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.51
 p-value of test no 46                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.01
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.36
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.31
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.74
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.44
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.42
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.59
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1411.32
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6871.09
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.67
 p-value of test no 58                 :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
 p-value of test no 59                 :    0.9952
 
 Anderson-Darling statistic = A2       :    4.64
 p-value of test no 60                 :  4.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   12.96
 p-value of test no 61                 :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.82
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.22
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.91
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.33
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45754
 p-value of test no 70                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869754
   j =  1                              :        399908497
   j =  2                              :            45744
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45859
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869859
   j =  1                              :        399908283
   j =  2                              :            45857
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 79                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 117                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.38
 p-value of test no 119                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.67
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.66
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.75
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.96
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.42
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.87
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.76
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.61
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.12
 p-value of test no 134                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.70
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.59
 p-value of test no 136                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 138                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.16
 p-value of test no 141                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17234.08
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.25
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.01
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.08
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.62
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.99
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.45
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.53
 p-value of test no 152                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.94
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.11
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.14
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.97
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.89
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.24
 p-value of test no 158                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.19
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.30
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.86
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.57
 p-value of test no 162                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.15
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.16
 p-value of test no 164                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.97
 p-value of test no 165                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.15
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.50
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.44
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.19
 p-value of test no 169                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.42
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.58
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.87
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4936.63
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.30
 p-value of test no 174                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.61
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   36.14
 p-value of test no 176                :  3.1e-4    *****
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -4.82
 p-value of test no 177                : 1 -  7.1e-7    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.55
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.61
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 188                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 190                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 192                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.55
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.11
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.32
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.20
 p-value of test no 207                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 209                :    0.94
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9773.20
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 214                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9976.94
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.098
 p-value of test no 217                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 221                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.70
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 225                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4715.90
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4013.01
 p-value of test no 227                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4133.04
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11886.60
 p-value of test no 229                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12011.99
 p-value of test no 230                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.78
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000065167
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.52
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  7999867842
 
 Normal statistic for number of bits   :   -1.04
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.38
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 238                :    0.40
 
 Sample variance                       :    0.90
 p-value of test no 239                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 241                :    0.77
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.045
 p-value of test no 243                :    0.48
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 253                :    0.38
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.93
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  80  LinearComp, r = 0              1 -  7.1e-7
  80  LinearComp, r = 0               3.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35848
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 5                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 8                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5372
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 21                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    1.96
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     558
 p-value of test no 31                 :    0.96
 
 Stat. AD (mNP2)                       :    3.06
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.25
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.39
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.20
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 47                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.76
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.77
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.58
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.21
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.08
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 53                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.77
 p-value of test no 54                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.15
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1409.13
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7226.77
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.00
 p-value of test no 61                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.80
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.44
 p-value of test no 66                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.86
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4942.01
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45851
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869851
   j =  1                              :        399908302
   j =  2                              :            45843
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45335
 p-value of test no 71                 :    0.9945
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869335
   j =  1                              :        399909334
   j =  2                              :            45327
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 76                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 85                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 88                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 99                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 100                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 103                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    2.46
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 106                :  8.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 107                :    0.89
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 108                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.92e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.01
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.71
 p-value of test no 119                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.26
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.86
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.10
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.93
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.69
 p-value of test no 124                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.90
 p-value of test no 125                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.17
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 130                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   23.35
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.89
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.80
 p-value of test no 135                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    8.52
 p-value of test no 137                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  154.37
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.52
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.48
 p-value of test no 147                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.99
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.51
 p-value of test no 149                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.07
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.58
 p-value of test no 151                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.87
 p-value of test no 152                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.82
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.89
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.47
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.81
 p-value of test no 156                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.35
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.24
 p-value of test no 158                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.72
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.27
 p-value of test no 160                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.49
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.49
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.08
 p-value of test no 163                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.17
 p-value of test no 164                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.31
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.75
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.90
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4955.61
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.59
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.34
 p-value of test no 170                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.99
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.38
 p-value of test no 172                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4862.74
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.78
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.57
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.39
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.53
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.68
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.65
 p-value of test no 189                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 192                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.64
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.56
 p-value of test no 198                :    0.9916
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.51
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.07
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.62
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10044.28
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10050.69
 p-value of test no 215                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.47
 p-value of test no 216                :  6.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.40
 p-value of test no 217                :    0.9919
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 219                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 220                :    0.04
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5047.91
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.44
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.98
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.29
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11876.26
 p-value of test no 229                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11810.65
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.98
 p-value of test no 231                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000093865
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.01
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000036823
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 237                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.00
 p-value of test no 238                :    0.16
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.15
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.46
 p-value of test no 249                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 252                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:27.60
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35849
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 4                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997267
   j =  2                              :             1365
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 9                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 11                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7445
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4231
 p-value of test no 17                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7436
 p-value of test no 20                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.40
 p-value of test no 22                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     936
 p-value of test no 25                 :    0.12
 
 Stat. AD (mNP2)                       :    2.88
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 30                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     623
 p-value of test no 31                 :    0.18
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 33                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 35                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.58
 p-value of test no 41                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    4.40
 p-value of test no 42                 :  5.6e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     185
 p-value of test no 43                 :  3.2e-3
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.68
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.78
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.63
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.76
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.79
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.79
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.04
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.15
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.62
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7192.73
 p-value of test no 57                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.81
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.61
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.88
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.23
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5034.83
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45700
 p-value of test no 70                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869700
   j =  1                              :        399908602
   j =  2                              :            45696
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46202
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870202
   j =  1                              :        399907601
   j =  2                              :            46192
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 79                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 88                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 91                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 92                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
 p-value of test no 98                 :    0.9931
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.31
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 108                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.022
 p-value of test no 116                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.95
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.51
 p-value of test no 120                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.13
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.82
 p-value of test no 122                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.49
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.60
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.52
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.62
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.09
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.55
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.86
 p-value of test no 141                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17134.14
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.09
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.87
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.55
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.94
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.99
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 152                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.24
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.75
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.11
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.72
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.37
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.40
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.90
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.01
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.88
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.51
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  457.15
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.74
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.61
 p-value of test no 165                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.51
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.15
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.51
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.52
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.81
 p-value of test no 170                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.42
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.06
 p-value of test no 172                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.13
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.73
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.43
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.78
 p-value of test no 178                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.65
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 182                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.42
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.27
 p-value of test no 184                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.46
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.76
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.66
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.98
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 208                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.17
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10194.08
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.29
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 218                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.09
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.31
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4041.51
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4279.72
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11562.67
 p-value of test no 229                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11966.20
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.80
 p-value of test no 231                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000015175
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.59
 p-value of test no 233                :    0.9936
 
 
 -----------------------------------------------
 Total number of bits:  7999968780
 
 Normal statistic for number of bits   :   -0.25
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 236                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 237                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    0.48
 p-value of test no 239                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 243                :    0.62
 
 Sample variance                       :    0.43
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 248                :    0.14
 
 Sample variance                       :    0.86
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35850
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 6                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1426
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334546
   j =  1                              :        599997148
   j =  2                              :             1426
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 8                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5443
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7421
 p-value of test no 18                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 19                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 21                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 23                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.17
 p-value of test no 30                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.87
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 35                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     314
 p-value of test no 37                 :    0.22
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.34
 p-value of test no 41                 :  6.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.86
 p-value of test no 46                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.37
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.53
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   88.63
 p-value of test no 50                 :  2.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.61
 p-value of test no 52                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.48
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.45
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  461.31
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1337.76
 p-value of test no 56                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6989.43
 p-value of test no 57                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.99
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.22
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.04
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.38
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5008.89
 p-value of test no 68                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45679
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869679
   j =  1                              :        399908643
   j =  2                              :            45677
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45907
 p-value of test no 71                 :    0.45
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869907
   j =  1                              :        399908191
   j =  2                              :            45897
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 78                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 106                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.33e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 115                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 117                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.07
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.93
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.30
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.88
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.39
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.89
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.48
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.96
 p-value of test no 129                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 130                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.93
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.85
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.14
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    9.94
 p-value of test no 137                :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.65
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17316.91
 p-value of test no 145                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.71
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.67
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.08
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.89
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.92
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.77
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.46
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.67
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.14
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.43
 p-value of test no 155                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.43
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.77
 p-value of test no 157                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.70
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.06
 p-value of test no 159                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.91
 p-value of test no 160                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.92
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.73
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.33
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.88
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.58
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.16
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.27
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.77
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.36
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.39
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.73
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.18
 p-value of test no 172                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5177.25
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.54
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.24
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.98
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.92
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.19
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 182                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.071
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.52
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.18
 p-value of test no 188                :    0.88
 
 Sample variance                       :    1.66
 p-value of test no 189                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 192                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.94
 p-value of test no 196                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.08
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.91
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.88
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9947.13
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9693.55
 p-value of test no 215                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.50
 p-value of test no 218                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 221                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4754.94
 p-value of test no 222                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.47
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.11
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4210.53
 p-value of test no 227                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4275.06
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.06
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11625.77
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.40
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000063946
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.98
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  7999869351
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 234                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 243                :    0.11
 
 Sample variance                       :    2.03
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.36
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 250                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.77
 p-value of test no 254                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35851
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 10                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 11                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 18                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.20
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.67
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     617
 p-value of test no 31                 :    0.25
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.33
 p-value of test no 34                 :  6.3e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   20.65
 p-value of test no 46                 :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.02
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.03
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.91
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.51
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.90
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.50
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.64
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.34
 p-value of test no 55                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1406.11
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7070.51
 p-value of test no 57                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.30
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.94
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.98
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.52
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5064.49
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45944
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869944
   j =  1                              :        399908113
   j =  2                              :            45942
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46037
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870037
   j =  1                              :        399907928
   j =  2                              :            46033
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 72                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 79                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 90                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 102                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
 p-value of test no 113                :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 115                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.50
 p-value of test no 117                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 118                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.03
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.36
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.09
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.02
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.78
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.45
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.49
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 127                :    0.95
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.69
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.39
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.41
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.10
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 137                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 138                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.21
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 142                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.39
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.60
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.18
 p-value of test no 148                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.93
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.19
 p-value of test no 150                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.97
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.76
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.25
 p-value of test no 153                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.23
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.89
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.79
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.24
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.41
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.27
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.87
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.93
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.61
 p-value of test no 162                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.63
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.74
 p-value of test no 164                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.02
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.56
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.78
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4830.66
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.71
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.24
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.43
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.00
 p-value of test no 172                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.81
 p-value of test no 173                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.61
 p-value of test no 174                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.04
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.83
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.32
 p-value of test no 177                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.64
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 180                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.28
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.49
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 185                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 188                :    0.96
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
 p-value of test no 191                :    0.88
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
 p-value of test no 194                :    0.97
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.95
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.67
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.57
 p-value of test no 203                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.91
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10147.63
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.64
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.089
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.55
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 223                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 225                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4948.13
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3967.02
 p-value of test no 227                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.98
 p-value of test no 228                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11841.92
 p-value of test no 229                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.48
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.69
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000006457
 
 Normal statistic for number of bits   :   0.051
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.46
 p-value of test no 233                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999943982
 
 Normal statistic for number of bits   :   -0.44
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 236                :    0.87
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 237                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.90
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 246                :    0.20
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 247                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 248                :    0.14
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 252                :    0.9900
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.05
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:10.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35852
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 3                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 11                 :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 17                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 30                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.57
 p-value of test no 32                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.34
 p-value of test no 34                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    2.22
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.99
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.55
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.75
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.54
 p-value of test no 49                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.84
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.70
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.08
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.20
 p-value of test no 53                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.16
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  348.97
 p-value of test no 55                 :    0.9990
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1380.53
 p-value of test no 56                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7031.72
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 60                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.78
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.31
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.93
 p-value of test no 66                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.13
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5050.62
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908661
   j =  2                              :            45662
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45952
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869952
   j =  1                              :        399908099
   j =  2                              :            45946
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 76                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 94                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 98                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 106                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.26
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 116                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.46
 p-value of test no 119                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.29
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.11
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.22
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.09
 p-value of test no 123                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.91
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.47
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.76
 p-value of test no 129                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.70
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.58
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.50
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.28
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 144                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17396.40
 p-value of test no 145                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.74
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.44
 p-value of test no 147                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.94
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.70
 p-value of test no 149                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.62
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.39
 p-value of test no 151                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.40
 p-value of test no 152                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.65
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.75
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.61
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.91
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.74
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  446.97
 p-value of test no 158                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.19
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.87
 p-value of test no 160                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.80
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.51
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.20
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.25
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.85
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.24
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.57
 p-value of test no 167                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4954.33
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  337.68
 p-value of test no 169                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.81
 p-value of test no 170                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.93
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.93
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5164.66
 p-value of test no 173                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.24
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.04
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.54
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.41
 p-value of test no 178                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 179                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 182                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 183                :    0.02
 
 Sample variance                       :    1.58
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 188                :    0.77
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.55
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.11
 p-value of test no 198                :    0.93
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.67
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.71
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.04
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.35
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10086.63
 p-value of test no 215                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      : -2.43e-3
 p-value of test no 216                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.02
 p-value of test no 217                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.12
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4931.50
 p-value of test no 222                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.36
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4106.49
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.05
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11949.97
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.45
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.26
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999960524
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.44
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999910568
 
 Normal statistic for number of bits   :   -0.71
 p-value of test no 234                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 240                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    2.85
 p-value of test no 244                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 245                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.94
 p-value of test no 248                :    0.83
 
 Sample variance                       :    1.08
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.97
 p-value of test no 254                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:15.02
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35853
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 5                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 6                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 8                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 11                 :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 12                 :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5496
 p-value of test no 13                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 20                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.01
 p-value of test no 22                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 23                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    3.37
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.42
 p-value of test no 34                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     267
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    5.23
 p-value of test no 41                 :  2.5e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    1.59
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.98
 p-value of test no 45                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.94
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.15
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.78
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.99
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.94
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.88
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.93
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.91
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7026.16
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 60                 :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   58.99
 p-value of test no 61                 :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 62                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.83
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.13
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.02
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4996.52
 p-value of test no 68                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46001
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870001
   j =  1                              :        399908002
   j =  2                              :            45993
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45950
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869950
   j =  1                              :        399908100
   j =  2                              :            45950
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.92e-3
 p-value of test no 80                 :    0.9980
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 85                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.56
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 111                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.042
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.65
 p-value of test no 119                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.94
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.29
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.48
 p-value of test no 122                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.75
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.69
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.57
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.24
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.75
 p-value of test no 129                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.85
 p-value of test no 133                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.69
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  151.32
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17329.16
 p-value of test no 145                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.30
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.22
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.86
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.84
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.09
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.93
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.14
 p-value of test no 152                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.33
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.33
 p-value of test no 154                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.51
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.95
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.93
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.93
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.24
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 161                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.43
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.75
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.64
 p-value of test no 164                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.13
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.07
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  341.67
 p-value of test no 167                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5109.96
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.94
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.20
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.42
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  345.34
 p-value of test no 172                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.95
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.17
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.94
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.46
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.88
 p-value of test no 184                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.51
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.97
 p-value of test no 189                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 195                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.05
 p-value of test no 196                :    0.34
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 198                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.27
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.32
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10228.95
 p-value of test no 211                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.13
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.08
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.26
 p-value of test no 218                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4955.07
 p-value of test no 222                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 225                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.87
 p-value of test no 226                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4169.88
 p-value of test no 227                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4227.47
 p-value of test no 228                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11939.60
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11760.13
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.88
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000026860
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.94
 p-value of test no 233                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999938153
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
 p-value of test no 236                :    0.9940
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.01
 p-value of test no 238                :    0.98
 
 Sample variance                       :    1.31
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 243                :    0.10
 
 Sample variance                       :    1.47
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.60
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 252                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    1.07
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:11.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35854
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 4                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 6                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 8                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 12                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 15                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7386
 p-value of test no 20                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.19
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 26                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    3.85
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.54
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.54
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 40                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 42                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.77
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.76
 p-value of test no 48                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.31
 p-value of test no 49                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.29
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.00
 p-value of test no 51                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.06
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   76.47
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.36
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.69
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.15
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7168.91
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 60                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.56
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 62                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 64                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.94
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.67
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.05
 p-value of test no 67                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5016.23
 p-value of test no 68                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908183
   j =  2                              :            45898
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45823
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869823
   j =  1                              :        399908357
   j =  2                              :            45817
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 73                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 74                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 77                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 85                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 88                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 97                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
 p-value of test no 112                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.97
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.83
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.32
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.39
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.46
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.53
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.75
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.67
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.89
 p-value of test no 129                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 132                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 135                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.49
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 140                :    0.9945
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.32
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 144                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17853.86
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   65.02
 p-value of test no 146                :  2.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.03
 p-value of test no 147                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.75
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.11
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.82
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.31
 p-value of test no 151                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.15
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.91
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.23
 p-value of test no 154                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.61
 p-value of test no 155                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.51
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.20
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.70
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.07
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.43
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.85
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.61
 p-value of test no 163                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.35
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.77
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.15
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.99
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.78
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.96
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.25
 p-value of test no 170                :    0.9903
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.76
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.61
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.47
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.51
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.85
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.70
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.77
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.13
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.84
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 192                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 195                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.14
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.28
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.30
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.32
 p-value of test no 207                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.71
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9850.60
 p-value of test no 211                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10016.40
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.41
 p-value of test no 216                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.51
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4746.10
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4998.51
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.02
 p-value of test no 227                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4008.98
 p-value of test no 228                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11683.38
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.28
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.25
 p-value of test no 231                :    0.83
 
 
 -----------------------------------------------
 Total number of bits:  7999996140
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.76
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000100303
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.024
 p-value of test no 238                :    0.49
 
 Sample variance                       :    0.29
 p-value of test no 239                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.54
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.98
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.95
 p-value of test no 248                :    0.17
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:40.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35855
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 9                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 10                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5439
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 20                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7334
 p-value of test no 21                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 22                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.97
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 29                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.37
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 34                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    4.03
 p-value of test no 38                 :  8.4e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 39                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.03
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.82
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.86
 p-value of test no 48                 :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.48
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.90
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.68
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.17
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  248.57
 p-value of test no 54                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.49
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1535.06
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7153.68
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.20
 p-value of test no 61                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 63                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.81
 p-value of test no 65                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.16
 p-value of test no 66                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  114.95
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.81
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46227
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870227
   j =  1                              :        399907550
   j =  2                              :            46219
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45999
 p-value of test no 71                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869999
   j =  1                              :        399908007
   j =  2                              :            45989
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    2.60
 p-value of test no 74                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 79                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 81                 :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 86                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 88                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 92                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 95                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 105                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.42
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.93
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.64
 p-value of test no 120                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.49
 p-value of test no 121                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.48
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.90
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.34
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.54
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.06
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.08
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.63
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.49
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.09
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.06
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.89
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.98
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.43
 p-value of test no 149                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.53
 p-value of test no 150                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.52
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.89
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.65
 p-value of test no 153                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.47
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.19
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.11
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  561.74
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  100.80
 p-value of test no 159                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.24
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.22
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.66
 p-value of test no 162                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.71
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.92
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.47
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.18
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4829.56
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.60
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.82
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.43
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.70
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.71
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.95
 p-value of test no 174                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.50
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.53
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.47
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.29
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.14
 p-value of test no 179                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 182                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.65
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.14
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 192                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
 p-value of test no 194                :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.99
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.60
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 202                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.67
 p-value of test no 203                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.55
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.22
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10085.43
 p-value of test no 211                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.85
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.50
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 216                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.46
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.32
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 223                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5013.67
 p-value of test no 226                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4135.11
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.34
 p-value of test no 228                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12099.32
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.43
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.61
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000133099
 
 Normal statistic for number of bits   :    1.05
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.33
 p-value of test no 233                :    0.96
 
 
 -----------------------------------------------
 Total number of bits:  8000042535
 
 Normal statistic for number of bits   :    0.34
 p-value of test no 234                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 235                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 238                :    0.41
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.17
 p-value of test no 244                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.77
 p-value of test no 249                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    0.69
 p-value of test no 254                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:49.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35856
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1268
 p-value of test no 12                 :    0.9956
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334388
   j =  1                              :        599997464
   j =  2                              :             1268
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5358
 p-value of test no 13                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4189
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7495
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7464
 p-value of test no 21                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 23                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 24                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     865
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 27                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 30                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.91
 p-value of test no 36                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.18
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.56
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.09
 p-value of test no 48                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.91
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.16
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.49
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.81
 p-value of test no 52                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.59
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.85
 p-value of test no 54                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.96
 p-value of test no 55                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.45
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7000.81
 p-value of test no 57                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.50
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.85
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 63                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.10
 p-value of test no 65                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.77
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.82
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5190.39
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45654
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869654
   j =  1                              :        399908694
   j =  2                              :            45650
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45637
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869637
   j =  1                              :        399908730
   j =  2                              :            45629
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 74                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 77                 :  6.3e-4    *****
 
 Anderson-Darling statistic = A2       :    4.08
 p-value of test no 78                 :  8.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
 p-value of test no 87                 :    0.9923
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 88                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 99                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 116                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.84
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.28
 p-value of test no 120                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.94
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.69
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.68
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.59
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.18
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.70
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.39
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.20
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.73
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.12
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 140                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.92
 p-value of test no 141                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17429.20
 p-value of test no 145                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.53
 p-value of test no 146                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.07
 p-value of test no 147                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 148                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.00
 p-value of test no 149                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.73
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.29
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.34
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.51
 p-value of test no 153                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.99
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.39
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.81
 p-value of test no 156                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.18
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.76
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.77
 p-value of test no 159                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.34
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.13
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.03
 p-value of test no 162                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.65
 p-value of test no 163                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.23
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.61
 p-value of test no 165                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.48
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  434.92
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.52
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.97
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.22
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.15
 p-value of test no 171                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  446.53
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.07
 p-value of test no 173                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.07
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.14
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.40
 p-value of test no 176                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.27
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.91
 p-value of test no 179                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.16
 p-value of test no 183                :    0.88
 
 Sample variance                       :    1.44
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.63
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
 p-value of test no 194                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.70
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.49
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 205                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.50
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 209                :    0.07
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10131.63
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 214                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9786.92
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.076
 p-value of test no 216                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.58
 p-value of test no 222                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4978.38
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.73
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.09
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12039.46
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11877.02
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.71
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999948263
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.29
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999922181
 
 Normal statistic for number of bits   :   -0.62
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 236                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.47
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 248                :    0.34
 
 Sample variance                       :    0.95
 p-value of test no 249                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.67
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:49.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35857
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 8                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 11                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 12                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5423
 p-value of test no 13                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 15                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 18                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 23                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     878
 p-value of test no 25                 :    0.76
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 28                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 30                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     646
 p-value of test no 31                 :    0.03
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.46
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    2.23
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 41                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    3.00
 p-value of test no 44                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.27
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.98
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.51
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.72
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.72
 p-value of test no 51                 :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.17
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.79
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  184.82
 p-value of test no 54                 :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.52
 p-value of test no 55                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1450.88
 p-value of test no 56                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6936.94
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.03
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   62.15
 p-value of test no 65                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.75
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.22
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.75
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46252
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870252
   j =  1                              :        399907503
   j =  2                              :            46238
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908053
   j =  2                              :            45972
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 78                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 92                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 95                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 100                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 102                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 116                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.47
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.82
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.57
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.28
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.63
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.83
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.24
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.75
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.75
 p-value of test no 129                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.57
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.85
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.27
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.65
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.74
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 144                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17257.16
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.98
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.08
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.59
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.81
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.80
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.49
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.00
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.70
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.23
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.54
 p-value of test no 157                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.52
 p-value of test no 158                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.33
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.74
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.64
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.03
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  182.10
 p-value of test no 164                :  5.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.76
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.55
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.06
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.74
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.14
 p-value of test no 169                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.45
 p-value of test no 170                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.67
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.24
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5128.94
 p-value of test no 173                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.21
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.64
 p-value of test no 175                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.94
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 177                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.42
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.83
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    1.12
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.21
 p-value of test no 188                :    0.42
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
 p-value of test no 194                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 195                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.49
 p-value of test no 196                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.76
 p-value of test no 198                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.86
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.20
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9930.38
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.36
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.08
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.31
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 221                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.08
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.21
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.52
 p-value of test no 227                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.37
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.57
 p-value of test no 229                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11980.51
 p-value of test no 230                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.15
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000009091
 
 Normal statistic for number of bits   :   0.072
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.01
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000232228
 
 Normal statistic for number of bits   :    1.84
 p-value of test no 234                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 236                :    0.05
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 237                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.01
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 243                :    0.49
 
 Sample variance                       :    0.52
 p-value of test no 244                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 248                :    0.21
 
 Sample variance                       :    1.46
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 251                :    0.80
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.71
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:13.70
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35858
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 12                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5379
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 18                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.08
 p-value of test no 24                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     956
 p-value of test no 25                 :    0.03
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.50
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     264
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 38                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    1.98
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.21
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.79
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.61
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.35
 p-value of test no 49                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.18
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.76
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.00
 p-value of test no 52                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.21
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.56
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.26
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.97
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.05
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.92
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 64                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.12
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.81
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.33
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5094.33
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46004
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870004
   j =  1                              :        399907997
   j =  2                              :            45994
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46164
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870164
   j =  1                              :        399907674
   j =  2                              :            46160
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 79                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 81                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 102                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
 p-value of test no 106                :    0.9926
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.46e-4
 p-value of test no 112                :  8.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    4.67
 p-value of test no 114                :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.52
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.85
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 117                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 118                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   87.33
 p-value of test no 119                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.14
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.37
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.13
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.12
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.12
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.78
 p-value of test no 125                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.95
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 130                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.79
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.18
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.66
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.75
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 142                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17636.28
 p-value of test no 145                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.29
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.48
 p-value of test no 147                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.27
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.93
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.43
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.37
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.74
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.41
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.00
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.38
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.44
 p-value of test no 157                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  450.39
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.31
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.25
 p-value of test no 160                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.47
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.39
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.59
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.78
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.16
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.66
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.40
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.10
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.12
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.79
 p-value of test no 170                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.38
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.99
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.60
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.50
 p-value of test no 175                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.88
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.58
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.91
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 183                :    0.35
 
 Sample variance                       :    1.66
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.38
 p-value of test no 189                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
 p-value of test no 191                :    0.94
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.59
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.41
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.18
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 204                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  153.95
 p-value of test no 207                :    0.9933
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10093.54
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 214                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.56
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 221                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5058.18
 p-value of test no 222                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4929.10
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4071.13
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.40
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11978.60
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11743.97
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   31.77
 p-value of test no 231                :    0.9932
 
 
 -----------------------------------------------
 Total number of bits:  7999946715
 
 Normal statistic for number of bits   :   -0.42
 p-value of test no 232                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.24
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000021082
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 235                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 237                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 240                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.72
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.23
 p-value of test no 244                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 248                :    0.25
 
 Sample variance                       :    1.12
 p-value of test no 249                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 253                :    0.94
 
 Sample variance                       :    2.67
 p-value of test no 254                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:02.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35859
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 7                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 12                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5561
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4216
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 17                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 23                 :    0.9985
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.13
 p-value of test no 28                 :    0.9996    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 33                 :    0.9993    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.17
 p-value of test no 34                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    4.06
 p-value of test no 36                 :  8.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     263
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.18
 p-value of test no 39                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.61
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.33
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 42                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 46                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.98
 p-value of test no 47                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.31
 p-value of test no 48                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.90
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.60
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.40
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.00
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.06
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.73
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1447.26
 p-value of test no 56                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7143.07
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.65
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.37
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.94
 p-value of test no 66                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.32
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5090.37
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46103
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870103
   j =  1                              :        399907795
   j =  2                              :            46101
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907872
   j =  2                              :            46055
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 79                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 88                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.74
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 102                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
 p-value of test no 113                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 115                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 116                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.06
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.75
 p-value of test no 119                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.31
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.63
 p-value of test no 121                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.85
 p-value of test no 122                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.74
 p-value of test no 123                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.77
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.83
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 128                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.16
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.22
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.24
 p-value of test no 134                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.80
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 138                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  115.88
 p-value of test no 141                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17437.33
 p-value of test no 145                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.02
 p-value of test no 146                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.08
 p-value of test no 147                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.46
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.56
 p-value of test no 149                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.37
 p-value of test no 150                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.40
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.73
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.27
 p-value of test no 154                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.57
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.44
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.38
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.59
 p-value of test no 158                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.45
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.79
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.66
 p-value of test no 162                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  503.75
 p-value of test no 163                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.97
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.93
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.05
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.66
 p-value of test no 167                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4917.29
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.55
 p-value of test no 169                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.40
 p-value of test no 170                :  7.1e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.87
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.27
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5087.51
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.68
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.96
 p-value of test no 175                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.73
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.62
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.21
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.73
 
 Sample variance                       :    0.43
 p-value of test no 189                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
 p-value of test no 191                :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.70
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.63
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.46
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.09
 p-value of test no 211                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9787.40
 p-value of test no 215                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.17
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.027
 p-value of test no 218                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.04
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.22
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3990.20
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.31
 p-value of test no 228                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.39
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.98
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.51
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999972959
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.23
 p-value of test no 233                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  8000082423
 
 Normal statistic for number of bits   :    0.65
 p-value of test no 234                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 235                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.61
 p-value of test no 239                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 242                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.20
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.53e-3
 p-value of test no 250                :    0.9984
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.58
 p-value of test no 253                :  4.9e-3
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:59.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs NP, t = 5            0.9996 
  23  ClosePairs mNP2S, t = 5         0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35860
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 5                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 7                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 11                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4282
 p-value of test no 17                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 18                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 19                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7272
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.20
 p-value of test no 23                 :    0.9914
 
 Test on the Nm values of W_{n,i}(mNP1):    3.29
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     852
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 29                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    3.65
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     656
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 35                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.73
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.43
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.08
 p-value of test no 48                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.86
 p-value of test no 49                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.97
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.27
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.43
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.86
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.86
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.40
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1439.04
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6964.11
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 60                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.41
 p-value of test no 61                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 64                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.29
 p-value of test no 65                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.96
 p-value of test no 66                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.90
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4903.37
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 70                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908337
   j =  2                              :            45827
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45665
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869665
   j =  1                              :        399908672
   j =  2                              :            45661
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 95                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 100                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 104                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 108                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 111                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
 p-value of test no 112                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 113                :    0.65
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 114                :    0.9957
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 118                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.76
 p-value of test no 119                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.73
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.42
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.06
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.03
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.74
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 127                :    0.87
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.36
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 132                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.95
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 134                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.06
 p-value of test no 135                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 138                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.02
 p-value of test no 141                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17563.02
 p-value of test no 145                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.15
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.15
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.25
 p-value of test no 148                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.85
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.25
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.76
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.20
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.58
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.18
 p-value of test no 155                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.35
 p-value of test no 156                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.94
 p-value of test no 157                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.99
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.21
 p-value of test no 159                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.78
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.60
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.73
 p-value of test no 162                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.33
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.87
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.82
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.93
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.63
 p-value of test no 167                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4850.57
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  336.40
 p-value of test no 169                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.63
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.65
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.65
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.58
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.13
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.01
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.25
 p-value of test no 176                :    0.9935
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.45
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 188                :    0.29
 
 Sample variance                       :    0.78
 p-value of test no 189                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   28.49
 p-value of test no 196                :  3.9e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.24
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 204                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.90
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.46
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10223.86
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 220                :    0.98
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4750.34
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4950.90
 p-value of test no 226                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4229.83
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.56
 p-value of test no 228                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11787.77
 p-value of test no 229                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11926.79
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.08
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999973538
 
 Normal statistic for number of bits   :   -0.21
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.65
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000118891
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 247                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 248                :    0.24
 
 Sample variance                       :    0.34
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.39
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    2.59
 p-value of test no 254                :  5.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:14.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  86  LongestHeadRun, r = 0           3.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35861
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 3                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 4                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 5                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 6                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 7                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1283
 p-value of test no 10                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334403
   j =  1                              :        599997434
   j =  2                              :             1283
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 14                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.11
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 33                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 34                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    3.04
 p-value of test no 39                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.87
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.36
 p-value of test no 47                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.23
 p-value of test no 48                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.35
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.06
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.30
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.31
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.14
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  221.15
 p-value of test no 54                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.44
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.70
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7124.32
 p-value of test no 57                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 60                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.30
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 64                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.70
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.98
 p-value of test no 66                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.51
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.19
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45717
 p-value of test no 70                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869717
   j =  1                              :        399908568
   j =  2                              :            45713
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908316
   j =  2                              :            45836
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 74                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.37
 p-value of test no 115                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.52
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.70
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.42
 p-value of test no 121                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.28
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   70.13
 p-value of test no 123                :  8.2e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.72
 p-value of test no 124                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.64
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.27
 p-value of test no 129                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.74
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.11
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 139                :    0.84
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.95
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17670.02
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.34
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.09
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.01
 p-value of test no 148                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.86
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.56
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.22
 p-value of test no 151                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.47
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.39
 p-value of test no 153                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.46
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.47
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.29
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.13
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.81
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.34
 p-value of test no 159                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.19
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.84
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.11
 p-value of test no 162                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.24
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.95
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.91
 p-value of test no 165                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.65
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.52
 p-value of test no 167                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.38
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.05
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.84
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.48
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.69
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4795.52
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.81
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  240.34
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.22
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.86
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.02
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.55
 p-value of test no 179                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 186                :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.83
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
 p-value of test no 194                :    0.72
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.41
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.41
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 201                :    0.93
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 202                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.42
 p-value of test no 203                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.54
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10089.47
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9866.83
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.81
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.50
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4876.87
 p-value of test no 226                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.81
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4160.80
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.99
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.73
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.90
 p-value of test no 231                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999870134
 
 Normal statistic for number of bits   :   -1.03
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.50
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  7999886712
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 238                :    0.56
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.63
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 243                :    0.67
 
 Sample variance                       :    0.70
 p-value of test no 244                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 246                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 248                :    0.43
 
 Sample variance                       :    2.35
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 252                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:24.01
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  63  WeightDistrib, r = 10           8.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35862
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5503
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 16                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 18                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7226
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     639
 p-value of test no 31                 :    0.06
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 32                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 33                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.21
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     282
 p-value of test no 37                 :    0.84
 
 Stat. AD (mNP2)                       :    1.16
 p-value of test no 38                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 41                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.16
 p-value of test no 42                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     178
 p-value of test no 43                 :    0.01
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.76
 p-value of test no 46                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.91
 p-value of test no 47                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.17
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.90
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.53
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.77
 p-value of test no 51                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.73
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.61
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.68
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.31
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.74
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.21
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.39
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.00
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4974.47
 p-value of test no 68                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45954
 p-value of test no 70                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869954
   j =  1                              :        399908092
   j =  2                              :            45954
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45622
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869622
   j =  1                              :        399908760
   j =  2                              :            45614
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 78                 :    0.9923
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 86                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 93                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 98                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 100                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 108                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 109                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
 p-value of test no 112                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 115                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 117                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 118                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.96
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.77
 p-value of test no 120                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.61
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.09
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   59.61
 p-value of test no 123                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.97
 p-value of test no 125                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.35
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.97
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.10
 p-value of test no 135                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.63
 p-value of test no 136                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 138                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.73
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 140                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.47
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17499.17
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.11
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.18
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.88
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.96
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.56
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.63
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.05
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.68
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.43
 p-value of test no 154                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.71
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.87
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.85
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.07
 p-value of test no 158                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.77
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.94
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.39
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.89
 p-value of test no 162                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.18
 p-value of test no 163                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.96
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.26
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.64
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.79
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.58
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.31
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.28
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.96
 p-value of test no 171                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.30
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.04
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.34
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.42
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.11
 p-value of test no 176                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.57
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.19
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.033
 p-value of test no 183                :    0.49
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 185                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 187                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.78
 p-value of test no 188                :    0.96
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.61
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.10
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.44
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.21
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.91
 p-value of test no 207                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.62
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.71
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 218                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 221                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.55
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.14
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.00
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4142.17
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11749.43
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11593.04
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.57
 p-value of test no 231                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999980087
 
 Normal statistic for number of bits   :   -0.16
 p-value of test no 232                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.17
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000040066
 
 Normal statistic for number of bits   :    0.32
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.63
 p-value of test no 238                :    0.95
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 248                :    0.09
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.16
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 252                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.88
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:18.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35863
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 4                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 9                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 10                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 12                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5307
 p-value of test no 13                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4481
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4209
 p-value of test no 17                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 20                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 21                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 23                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     882
 p-value of test no 25                 :    0.72
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.66
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     561
 p-value of test no 31                 :    0.94
 
 Stat. AD (mNP2)                       :    0.19
 p-value of test no 32                 :    0.9923
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.53
 p-value of test no 39                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 41                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 45                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.13
 p-value of test no 46                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.87
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.22
 p-value of test no 48                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.12
 p-value of test no 49                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.91
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.59
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.46
 p-value of test no 52                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.79
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.78
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  412.09
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1392.48
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7158.86
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.07
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.21
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.86
 p-value of test no 66                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.38
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5101.02
 p-value of test no 68                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908228
   j =  2                              :            45886
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45635
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869635
   j =  1                              :        399908733
   j =  2                              :            45629
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 77                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 78                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 88                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.96
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.24
 p-value of test no 119                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.37
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.92
 p-value of test no 121                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.14
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.13
 p-value of test no 123                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.68
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.23
 p-value of test no 125                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.26
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.57
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 132                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.43
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 140                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.33
 p-value of test no 141                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.46
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 144                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17504.95
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.51
 p-value of test no 146                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   60.92
 p-value of test no 147                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.00
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.79
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.83
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.63
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.39
 p-value of test no 152                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.79
 p-value of test no 153                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.64
 p-value of test no 154                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 155                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.38
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.82
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.50
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.59
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.59
 p-value of test no 160                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.50
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.83
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.47
 p-value of test no 163                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.10
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.71
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.27
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.87
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5021.96
 p-value of test no 168                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.94
 p-value of test no 169                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.87
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.94
 p-value of test no 171                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.83
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5270.78
 p-value of test no 173                :  3.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  325.76
 p-value of test no 174                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.18
 p-value of test no 175                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.15
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.65
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.56
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 180                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.41
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 183                :    0.38
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 188                :    0.42
 
 Sample variance                       :    1.53
 p-value of test no 189                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
 p-value of test no 191                :    0.57
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.64
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.52
 p-value of test no 198                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.68
 p-value of test no 203                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  168.89
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9892.90
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 214                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9799.84
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.78
 p-value of test no 217                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4856.32
 p-value of test no 222                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.63
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.05
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4101.49
 p-value of test no 227                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.65
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.78
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.75
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.78
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999909068
 
 Normal statistic for number of bits   :   -0.72
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.73
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000053806
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 237                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 238                :    0.89
 
 Sample variance                       :    0.88
 p-value of test no 239                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 242                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 243                :    0.40
 
 Sample variance                       :    2.12
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 247                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.82
 p-value of test no 249                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 250                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 253                :    0.39
 
 Sample variance                       :    1.23
 p-value of test no 254                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:29.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35864
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 4                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 6                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 7                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 9                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 10                 :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 12                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5564
 p-value of test no 13                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 15                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7493
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 22                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    2.52
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 34                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.34
 p-value of test no 39                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 40                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.75
 p-value of test no 41                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    3.00
 p-value of test no 42                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     127
 p-value of test no 43                 :    0.97
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.86
 p-value of test no 46                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.74
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.98
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.38
 p-value of test no 51                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.21
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.42
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.49
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.38
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.29
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6830.92
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 60                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.77
 p-value of test no 61                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.65
 p-value of test no 65                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.10
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4922.78
 p-value of test no 68                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46216
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870216
   j =  1                              :        399907572
   j =  2                              :            46208
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908314
   j =  2                              :            45834
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 80                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 84                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 99                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.25
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 118                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.05
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.18
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.47
 p-value of test no 121                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.39
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.29
 p-value of test no 123                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.70
 p-value of test no 124                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.02
 p-value of test no 125                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.00
 p-value of test no 129                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.60
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.77
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.35
 p-value of test no 135                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.26
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 140                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.08
 p-value of test no 141                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17485.13
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.06
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.16
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.09
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.37
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.57
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.84
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.25
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.48
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.69
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.64
 p-value of test no 155                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.29
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.42
 p-value of test no 157                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.72
 p-value of test no 158                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.00
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.27
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.61
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.31
 p-value of test no 162                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.23
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.61
 p-value of test no 164                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.86
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.74
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.30
 p-value of test no 167                :    0.9902
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4995.75
 p-value of test no 168                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.27
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.38
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.96
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.56
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.22
 p-value of test no 173                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.51
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  215.99
 p-value of test no 175                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.13
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.42
 p-value of test no 177                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.42
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.015
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 180                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.48
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.49
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 188                :    0.26
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 192                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 195                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.10
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  243.52
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.89
 p-value of test no 207                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 208                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10034.92
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.93
 p-value of test no 215                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 216                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.77
 p-value of test no 218                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.39
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 221                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.18
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 224                :    0.02
 
 Anderson-Darling statistic = A2       :    2.52
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.68
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4028.11
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.13
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.22
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.40
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.64
 p-value of test no 231                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  8000062713
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.16
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999932237
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 243                :    0.82
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.53
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.94
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 250                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 251                :    0.76
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.86
 p-value of test no 254                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:57.96
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35865
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 5                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 6                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 9                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 10                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5353
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4327
 p-value of test no 14                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7170
 p-value of test no 15                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7182
 p-value of test no 19                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 22                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.95
 p-value of test no 24                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     961
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    2.31
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.96
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.50
 p-value of test no 29                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 33                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 41                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.83
 p-value of test no 44                 :    0.46
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.51
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.64
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.58
 p-value of test no 48                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.17
 p-value of test no 49                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.22
 p-value of test no 50                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.07
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.01
 p-value of test no 53                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.50
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  480.59
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.78
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.41
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.81
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.86
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.16
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.34
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5029.23
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46101
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870101
   j =  1                              :        399907801
   j =  2                              :            46095
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46096
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870096
   j =  1                              :        399907811
   j =  2                              :            46090
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 88                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 98                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 104                :    0.9946
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 106                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
 p-value of test no 109                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
 p-value of test no 110                :    0.31
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 111                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 114                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.38
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.30
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.03
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.57
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.52
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   18.97
 p-value of test no 123                :    0.9939
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.55
 p-value of test no 124                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   45.78
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 128                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.00
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.63
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.52
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.45
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.18
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 144                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17460.27
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.03
 p-value of test no 146                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.38
 p-value of test no 147                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.45
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.46
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.34
 p-value of test no 152                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.41
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.27
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.16
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.09
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.68
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.51
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.16
 p-value of test no 160                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.65
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.01
 p-value of test no 162                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.28
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.72
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.36
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.02
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.79
 p-value of test no 167                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4839.45
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.79
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.97
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.62
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.47
 p-value of test no 172                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5092.05
 p-value of test no 173                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.82
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.16
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.04
 p-value of test no 176                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 177                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.16
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.01
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 180                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.46
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 183                :    0.84
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 186                :    0.27
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.47
 p-value of test no 189                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.04
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.35
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.30
 p-value of test no 196                :    0.10
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.40
 p-value of test no 198                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 202                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.91
 p-value of test no 203                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.92
 p-value of test no 207                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 209                :    0.80
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9949.89
 p-value of test no 211                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.06
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 214                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10267.26
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.026
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.070
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 220                :    0.07
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 221                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5010.97
 p-value of test no 222                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.71
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4009.43
 p-value of test no 227                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.78
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.64
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11813.95
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.24
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000050383
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.26
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000097915
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 237                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    1.06
 p-value of test no 244                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 246                :    0.89
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 248                :    0.82
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.00
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.72
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35866
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 7                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 11                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 17                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7533
 p-value of test no 19                 :  6.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.05
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    3.23
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     569
 p-value of test no 31                 :    0.89
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    3.36
 p-value of test no 39                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 44                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.78
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.20
 p-value of test no 48                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.57
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.50
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.06
 p-value of test no 52                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.42
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  267.93
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.55
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.64
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6951.19
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.50
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.07
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.46
 p-value of test no 66                 :    0.9936
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  148.36
 p-value of test no 67                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4945.28
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45997
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869997
   j =  1                              :        399908012
   j =  2                              :            45985
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45803
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869803
   j =  1                              :        399908399
   j =  2                              :            45793
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 76                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 78                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.58
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 104                :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.79e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
 p-value of test no 113                :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.48
 p-value of test no 115                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.061
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.31
 p-value of test no 119                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.43
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.87
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.51
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.02
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.03
 p-value of test no 124                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   17.30
 p-value of test no 125                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.32
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 132                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.00
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.68
 p-value of test no 134                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.75
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 138                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 140                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.06
 p-value of test no 141                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 142                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17548.67
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.00
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.38
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.92
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.84
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.56
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.35
 p-value of test no 151                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.88
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.94
 p-value of test no 154                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.02
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.30
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.11
 p-value of test no 157                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.61
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.24
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.54
 p-value of test no 160                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.67
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.23
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.11
 p-value of test no 163                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.70
 p-value of test no 164                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.93
 p-value of test no 165                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.00
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.10
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5138.36
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.22
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.53
 p-value of test no 170                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.92
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.09
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4890.72
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.43
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.49
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.98
 p-value of test no 176                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.54
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.61
 p-value of test no 178                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.20
 p-value of test no 179                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 183                :    0.56
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 185                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 187                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.02
 p-value of test no 188                :    0.98
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 190                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 196                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.77
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.21
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 206                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.50
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 209                :    0.03
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10123.66
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.93
 p-value of test no 215                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 218                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.94
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.00
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4088.00
 p-value of test no 227                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4213.01
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11758.53
 p-value of test no 229                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11834.07
 p-value of test no 230                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.97
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  7999941321
 
 Normal statistic for number of bits   :   -0.46
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.31
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000000811
 
 Normal statistic for number of bits   : 6.41e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 238                :    0.42
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 248                :    0.42
 
 Sample variance                       :    0.62
 p-value of test no 249                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35867
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 4                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 8                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 9                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 10                 :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1463
 p-value of test no 11                 :  4.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334583
   j =  1                              :        599997074
   j =  2                              :             1463
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5303
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4414
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4298
 p-value of test no 17                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 19                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 22                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     929
 p-value of test no 25                 :    0.17
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 26                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.13
 p-value of test no 29                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.20
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 44                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.03
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.55
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.93
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.88
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.19
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.56
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.29
 p-value of test no 52                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.25
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  203.67
 p-value of test no 54                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.45
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.39
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7014.02
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 59                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.83
 p-value of test no 61                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 62                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   53.99
 p-value of test no 65                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.57
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.42
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4986.92
 p-value of test no 68                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45659
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869659
   j =  1                              :        399908684
   j =  2                              :            45655
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46129
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870129
   j =  1                              :        399907746
   j =  2                              :            46121
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 73                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 74                 :    0.9998    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 81                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 85                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 92                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.07
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
 p-value of test no 110                :    0.52
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 114                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.66
 p-value of test no 119                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.84
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.74
 p-value of test no 121                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.02
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.27
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.39
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.54
 p-value of test no 125                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 128                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.67
 p-value of test no 129                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.70
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.50
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.29
 p-value of test no 135                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.98
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  150.66
 p-value of test no 141                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17700.74
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.24
 p-value of test no 146                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.81
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.45
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.99
 p-value of test no 149                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.16
 p-value of test no 150                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.38
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.48
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.36
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.38
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.10
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.66
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.87
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.74
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.71
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.61
 p-value of test no 160                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.68
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.12
 p-value of test no 162                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  592.97
 p-value of test no 163                :  2.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.52
 p-value of test no 164                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.98
 p-value of test no 165                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.04
 p-value of test no 166                :    0.9939
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.77
 p-value of test no 167                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.66
 p-value of test no 168                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  436.24
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.45
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.87
 p-value of test no 171                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  334.81
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5086.65
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.15
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.47
 p-value of test no 175                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.82
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.13
 p-value of test no 177                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.82
 p-value of test no 178                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.043
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.08
 p-value of test no 189                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 195                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.84
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.15
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.05
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.08
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.39
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.68
 p-value of test no 207                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10055.17
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10120.03
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 216                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.55
 p-value of test no 217                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4781.46
 p-value of test no 222                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.36
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3938.05
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4312.74
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12014.19
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11815.13
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.12
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999985334
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.06
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000045844
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 236                :    0.01
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.59
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 242                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 243                :    0.58
 
 Sample variance                       :    0.45
 p-value of test no 244                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.42
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 247                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 248                :    0.29
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.34
 p-value of test no 254                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:18.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35868
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1270
 p-value of test no 11                 :    0.9948
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334390
   j =  1                              :        599997460
   j =  2                              :             1270
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 12                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5368
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7457
 p-value of test no 15                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4424
 p-value of test no 16                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 20                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.22
 p-value of test no 23                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 28                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    3.54
 p-value of test no 30                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     550
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 36                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.17
 p-value of test no 42                 :    0.9961
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.32
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.90
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.41
 p-value of test no 48                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.69
 p-value of test no 49                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.05
 p-value of test no 50                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.55
 p-value of test no 51                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.55
 p-value of test no 52                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.02
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.04
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  397.80
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.56
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7178.35
 p-value of test no 57                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 59                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 60                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.21
 p-value of test no 61                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 63                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.21
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.21
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.13
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.86
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45673
 p-value of test no 70                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869673
   j =  1                              :        399908658
   j =  2                              :            45665
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908275
   j =  2                              :            45861
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 72                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 85                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 111                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
 p-value of test no 112                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 114                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.96
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 116                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 117                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.66
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.16
 p-value of test no 120                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.12
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.35
 p-value of test no 122                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.48
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.45
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.41
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.03
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.06
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.77
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.14
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 143                :    0.02
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17687.82
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.12
 p-value of test no 146                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.41
 p-value of test no 147                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.04
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.86
 p-value of test no 149                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.37
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.09
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.06
 p-value of test no 152                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.10
 p-value of test no 153                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.42
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.57
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.87
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.45
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.86
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.33
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.13
 p-value of test no 160                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.25
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.71
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  444.76
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.39
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.20
 p-value of test no 165                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.38
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.84
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5028.63
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.98
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.15
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.18
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.31
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  413.13
 p-value of test no 174                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.29
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.41
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.73
 p-value of test no 177                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.50
 p-value of test no 178                :    0.57
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.95
 p-value of test no 179                :    0.83
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
 p-value of test no 181                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 183                :    0.97
 
 Sample variance                       :    1.29
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 186                :    0.88
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 187                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    1.28
 p-value of test no 189                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.17
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.13
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.40
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.34
 p-value of test no 207                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9797.09
 p-value of test no 211                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.39
 p-value of test no 215                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 216                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.09
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 225                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.16
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.61
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4024.67
 p-value of test no 228                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11741.34
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11867.70
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.07
 p-value of test no 231                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  7999882515
 
 Normal statistic for number of bits   :   -0.93
 p-value of test no 232                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   77.03
 p-value of test no 233                :    0.02
 
 
 -----------------------------------------------
 Total number of bits:  8000094867
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 236                :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.83
 p-value of test no 239                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.100
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 247                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.074
 p-value of test no 248                :    0.47
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    2.39
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:03.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35869
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 3                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 7                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5367
 p-value of test no 13                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 14                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4430
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    1.34
 p-value of test no 24                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     869
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.00
 p-value of test no 28                 :  8.9e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 29                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 30                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 40                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 41                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 42                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.16
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.06
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.90
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.94
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.42
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.36
 p-value of test no 51                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.93
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.72
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.95
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  439.14
 p-value of test no 55                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1505.82
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6934.52
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.75
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 63                 :  9.8e-3
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 64                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.67
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.47
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.33
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5075.96
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46077
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870077
   j =  1                              :        399907849
   j =  2                              :            46071
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45876
 p-value of test no 71                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869876
   j =  1                              :        399908252
   j =  2                              :            45868
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 76                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 85                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 94                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 99                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 102                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 106                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 108                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 7.24e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 114                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 115                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 118                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.25
 p-value of test no 119                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.71
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.54
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.08
 p-value of test no 123                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.67
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.14
 p-value of test no 125                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.52
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.65
 p-value of test no 133                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.98
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.47
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 140                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.80
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9935
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17453.52
 p-value of test no 145                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.85
 p-value of test no 146                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.74
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.87
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.37
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.73
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.18
 p-value of test no 151                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.43
 p-value of test no 153                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.28
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.34
 p-value of test no 155                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.70
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.39
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.10
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.20
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.21
 p-value of test no 160                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.63
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.47
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.73
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.45
 p-value of test no 164                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.68
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.29
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.83
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4937.27
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  396.67
 p-value of test no 169                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.31
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.12
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.70
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5060.45
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.14
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.99
 p-value of test no 175                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.19
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.40
 p-value of test no 178                :    0.89
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.39
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 182                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 183                :    0.89
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.14
 p-value of test no 188                :    0.87
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 191                :    0.45
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.65
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.75
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 202                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.30
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.38
 p-value of test no 207                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.84
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 214                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.90
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 216                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 218                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.71
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.67
 p-value of test no 226                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.20
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3973.14
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11822.13
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.93
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   33.94
 p-value of test no 231                :    0.99
 
 
 -----------------------------------------------
 Total number of bits:  8000143371
 
 Normal statistic for number of bits   :    1.13
 p-value of test no 232                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.45
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  7999988394
 
 Normal statistic for number of bits   :  -0.092
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 236                :    0.93
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 238                :    0.92
 
 Sample variance                       :    1.63
 p-value of test no 239                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.71
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 242                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 243                :    0.68
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 248                :    0.88
 
 Sample variance                       :    0.42
 p-value of test no 249                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.08
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 253                :    0.10
 
 Sample variance                       :    1.36
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.25
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:05.00
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35870
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 8                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 12                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5450
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4204
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 20                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7497
 p-value of test no 21                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    1.94
 p-value of test no 26                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    2.80
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 41                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 42                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.53
 p-value of test no 45                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.40
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.64
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.60
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.36
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.53
 p-value of test no 50                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.67
 p-value of test no 51                 :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.64
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.93
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  278.48
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.20
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1412.46
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7201.36
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 60                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.57
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.87
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.46
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5213.61
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45816
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869816
   j =  1                              :        399908370
   j =  2                              :            45812
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45833
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869833
   j =  1                              :        399908339
   j =  2                              :            45823
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 74                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 81                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 84                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 93                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 94                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 103                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
 p-value of test no 112                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.31
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.50
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.76
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.32
 p-value of test no 122                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.53
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.51
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.46
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 127                :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.13
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.88
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.86
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.95
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 140                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.25
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.42
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.64
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.28
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.18
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.68
 p-value of test no 149                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.86
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.30
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.76
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.95
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   36.96
 p-value of test no 155                :  3.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.93
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.39
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  548.48
 p-value of test no 158                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.97
 p-value of test no 159                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.77
 p-value of test no 160                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.55
 p-value of test no 161                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.26
 p-value of test no 162                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.31
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.68
 p-value of test no 164                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.22
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.97
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.89
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5140.68
 p-value of test no 168                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.83
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.51
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.01
 p-value of test no 171                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.08
 p-value of test no 172                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.06
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.30
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.32
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 180                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.43e-3
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 192                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 195                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.20
 p-value of test no 196                :    0.25
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.93
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.49
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.59
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 208                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 209                :  5.1e-3
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 210                :  7.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10343.20
 p-value of test no 211                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 213                :    0.09
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10092.85
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 218                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.36
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 224                :    0.89
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4705.99
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4204.63
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.02
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.07
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11968.09
 p-value of test no 230                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   69.28
 p-value of test no 231                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000039385
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.82
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999987788
 
 Normal statistic for number of bits   :  -0.097
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 237                :    0.9948
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.084
 p-value of test no 238                :    0.53
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 242                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.46
 p-value of test no 244                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 247                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.89
 p-value of test no 249                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.09
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:20.46
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35871
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 3                  :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 5                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 7                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 12                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 16                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 18                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 20                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     911
 p-value of test no 25                 :    0.36
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.30
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.62
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     275
 p-value of test no 37                 :    0.92
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.56
 p-value of test no 39                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.34
 p-value of test no 41                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 42                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 45                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.26
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.53
 p-value of test no 47                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.57
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.70
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.80
 p-value of test no 50                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.71
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.27
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.90
 p-value of test no 53                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.87
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.19
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.25
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.80
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.19
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.44
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.13
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.60
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.87
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45686
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869686
   j =  1                              :        399908630
   j =  2                              :            45682
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45647
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869647
   j =  1                              :        399908709
   j =  2                              :            45641
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 74                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 79                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 94                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 100                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.16
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.23
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 110                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.31e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.57
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.77
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.27
 p-value of test no 121                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.15
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.50
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.55
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.85
 p-value of test no 125                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.77
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 130                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 132                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.04
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.40
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.24
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.58
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17377.08
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.38
 p-value of test no 146                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.68
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.63
 p-value of test no 148                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.88
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.41
 p-value of test no 150                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.95
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.32
 p-value of test no 152                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.86
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.89
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.55
 p-value of test no 155                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.41
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.06
 p-value of test no 157                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.07
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.07
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.65
 p-value of test no 160                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.34
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.91
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.73
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.53
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.35
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.72
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.05
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.56
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.86
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.69
 p-value of test no 170                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.23
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.19
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4984.99
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.27
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.01
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.22
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.14
 p-value of test no 177                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.52
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.06
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.36
 p-value of test no 184                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.05
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.29e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 192                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.96
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.50
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.61
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.55
 p-value of test no 207                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9778.44
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9971.67
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 217                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.56
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5088.76
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3996.13
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.95
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.01
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.04
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.53
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999996134
 
 Normal statistic for number of bits   :  -0.031
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.80
 p-value of test no 233                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  8000038557
 
 Normal statistic for number of bits   :    0.30
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 235                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.49
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.33
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 253                :    0.36
 
 Sample variance                       :    1.99
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:46.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35872
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4227
 p-value of test no 14                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 18                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.25
 p-value of test no 22                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 26                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.99
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 30                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.40
 p-value of test no 35                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 38                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 40                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.90
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     168
 p-value of test no 43                 :    0.08
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.25
 p-value of test no 46                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.76
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.93
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.82
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.32
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.04
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.09
 p-value of test no 52                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.20
 p-value of test no 53                 :  6.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.03
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  374.65
 p-value of test no 55                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.34
 p-value of test no 56                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6966.08
 p-value of test no 57                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.31
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.30
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.41
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.09
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4959.11
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908453
   j =  2                              :            45769
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45821
 p-value of test no 71                 :    0.61
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869821
   j =  1                              :        399908363
   j =  2                              :            45811
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 74                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 76                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 77                 :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 81                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 86                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 92                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 102                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.05
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 108                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.51e-5
 p-value of test no 112                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.93
 p-value of test no 118                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.81
 p-value of test no 119                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.21
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.80
 p-value of test no 121                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.83
 p-value of test no 122                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.08
 p-value of test no 123                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.37
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.97
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.08
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.71
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.00
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.67
 p-value of test no 134                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.95
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.18
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 140                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.16
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 144                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17554.36
 p-value of test no 145                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.05
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.01
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.14
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.03
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.52
 p-value of test no 150                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.81
 p-value of test no 152                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.11
 p-value of test no 153                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.52
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.48
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.55
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.67
 p-value of test no 157                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.37
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.67
 p-value of test no 159                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.94
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.71
 p-value of test no 161                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.91
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.60
 p-value of test no 163                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.01
 p-value of test no 164                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.46
 p-value of test no 165                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.50
 p-value of test no 166                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.48
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.56
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.32
 p-value of test no 169                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.45
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.11
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.37
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4867.94
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.50
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.02
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.31
 p-value of test no 176                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.66
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.45
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.30
 
 Sample variance                       :    2.20
 p-value of test no 189                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
 p-value of test no 191                :    0.87
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
 p-value of test no 194                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.17
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.26
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 201                :    0.78
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.27
 p-value of test no 203                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.52
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9779.89
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 214                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.63
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 216                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -1.30e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.59
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.95
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9949
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.87
 p-value of test no 226                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.96
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.11
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11857.39
 p-value of test no 229                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11722.95
 p-value of test no 230                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.11
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000002923
 
 Normal statistic for number of bits   :   0.023
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.67
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000031171
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 242                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 251                :    0.17
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 253                :    0.16
 
 Sample variance                       :    0.59
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:05.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35873
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 6                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1307
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334427
   j =  1                              :        599997386
   j =  2                              :             1307
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4427
 p-value of test no 17                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 18                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7531
 p-value of test no 19                 :  6.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7467
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 21                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 24                 :    0.9913
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 27                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 30                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     644
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 33                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 39                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.33
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   17.59
 p-value of test no 47                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.73
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.71
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.28
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.51
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.42
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  204.85
 p-value of test no 54                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.18
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.84
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6906.04
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 58                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
 p-value of test no 59                 :    0.9975
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   18.93
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.28
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.65
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.78
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5135.26
 p-value of test no 68                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45778
 p-value of test no 70                 :    0.68
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869778
   j =  1                              :        399908446
   j =  2                              :            45774
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45504
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869504
   j =  1                              :        399908998
   j =  2                              :            45492
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 74                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 76                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 83                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 85                 :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 95                 :    0.9966
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 102                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 103                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
 p-value of test no 112                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.64
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.34
 p-value of test no 119                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.23
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.55
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.89
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.70
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.28
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.56
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 128                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.23
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.64
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.64
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 140                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.38
 p-value of test no 141                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17472.49
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.60
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.67
 p-value of test no 147                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.62
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.24
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.43
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.93
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.58
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.96
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.60
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.97
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.81
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.05
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.39
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.93
 p-value of test no 159                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.66
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.63
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.72
 p-value of test no 162                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  445.67
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.84
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.46
 p-value of test no 165                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.15
 p-value of test no 166                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.08
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4893.23
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.92
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.35
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.27
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.43
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4957.35
 p-value of test no 173                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.25
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.92
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.52
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.59
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.50
 p-value of test no 178                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 183                :    0.59
 
 Sample variance                       :    1.30
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.71
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 192                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
 p-value of test no 194                :    0.94
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.03
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.35
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 206                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.61
 p-value of test no 207                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9901.71
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.19
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 214                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.41
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.03
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 223                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 224                :    0.87
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 225                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4701.44
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.81
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4221.03
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11943.89
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.15
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.35
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999872402
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.39
 p-value of test no 233                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  7999962777
 
 Normal statistic for number of bits   :   -0.29
 p-value of test no 234                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 237                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 238                :    0.60
 
 Sample variance                       :    1.16
 p-value of test no 239                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.73
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 248                :    0.75
 
 Sample variance                       :    2.32
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.50
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.57
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:43.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35874
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 3                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 4                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 8                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 9                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 14                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7318
 p-value of test no 15                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4326
 p-value of test no 16                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7346
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7298
 p-value of test no 21                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 22                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 24                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 27                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.33
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 32                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.68
 p-value of test no 33                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.59
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 36                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 38                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 39                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 45                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.43
 p-value of test no 46                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.28
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.85
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.55
 p-value of test no 50                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.56
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.16
 p-value of test no 53                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.18
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.54
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1466.28
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7095.20
 p-value of test no 57                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.95
 p-value of test no 61                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 63                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.75
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.21
 p-value of test no 66                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   86.44
 p-value of test no 67                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.27
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45312
 p-value of test no 70                 :    0.9960
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869312
   j =  1                              :        399909379
   j =  2                              :            45306
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 71                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908299
   j =  2                              :            45846
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 72                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 77                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 83                 :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 90                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 94                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 95                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 99                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 103                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 106                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 115                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 118                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.69
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.89
 p-value of test no 121                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.61
 p-value of test no 122                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.64
 p-value of test no 123                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.34
 p-value of test no 124                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.90
 p-value of test no 125                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 128                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.87
 p-value of test no 129                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 131                :    0.03
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.62
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.42
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.43
 p-value of test no 135                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.79
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 138                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    2.79
 p-value of test no 140                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  101.90
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17815.75
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.35
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.59
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.88
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.20
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.03
 p-value of test no 150                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.85
 p-value of test no 151                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.32
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 153                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.76
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.61
 p-value of test no 155                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.28
 p-value of test no 156                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.40
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.52
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  160.55
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.74
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.74
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.67
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.36
 p-value of test no 163                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.32
 p-value of test no 164                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.38
 p-value of test no 165                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.41
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.56
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.64
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.49
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.17
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.11
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  322.51
 p-value of test no 172                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.46
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.75
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.34
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.94
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.56
 p-value of test no 177                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.95
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 182                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 183                :    0.60
 
 Sample variance                       :    0.24
 p-value of test no 184                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 185                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 188                :    0.17
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.32
 p-value of test no 196                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.06
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.59
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 206                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.03
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.79
 p-value of test no 211                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 213                :    0.43
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 214                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10006.61
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.67
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.65
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4824.26
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.96
 p-value of test no 226                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3914.41
 p-value of test no 227                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.18
 p-value of test no 228                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11976.91
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11995.91
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.36
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999932279
 
 Normal statistic for number of bits   :   -0.54
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.73
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999986627
 
 Normal statistic for number of bits   :   -0.11
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    0.96
 p-value of test no 239                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.58
 
 Sample variance                       :    2.14
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 248                :    0.95
 
 Sample variance                       :    2.69
 p-value of test no 249                :  4.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:39.88
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35875
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 6                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 8                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 9                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4500
 p-value of test no 14                 :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4267
 p-value of test no 16                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7313
 p-value of test no 19                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.55
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 39                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.97
 p-value of test no 41                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 44                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.16
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.54
 p-value of test no 47                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.74
 p-value of test no 48                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.57
 p-value of test no 49                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.44
 p-value of test no 50                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.13
 p-value of test no 51                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.09
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.84
 p-value of test no 53                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.62
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.86
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1479.78
 p-value of test no 56                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7176.14
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 60                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.38
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.86
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.91
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.00
 p-value of test no 67                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5191.34
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45887
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869887
   j =  1                              :        399908228
   j =  2                              :            45883
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45974
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869974
   j =  1                              :        399908056
   j =  2                              :            45966
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 77                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 80                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 86                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 88                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 94                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 95                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 101                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 108                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
 p-value of test no 109                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
 p-value of test no 110                :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 115                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.90
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.28
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.58
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.80
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.92
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.02
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.61
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 127                :    0.90
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.58
 p-value of test no 129                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.46
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.85
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.39
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.65
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 138                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.18
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.61
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17296.80
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.42
 p-value of test no 146                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.46
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.63
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.24
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.99
 p-value of test no 150                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.88
 p-value of test no 151                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.75
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.46
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.21
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.66
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  199.01
 p-value of test no 156                :  2.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.45
 p-value of test no 157                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  439.91
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.27
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.73
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.40
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.89
 p-value of test no 163                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.74
 p-value of test no 164                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.14
 p-value of test no 165                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.35
 p-value of test no 166                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.17
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.29
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.78
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.13
 p-value of test no 170                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.94
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.73
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.82
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.52
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.32
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 177                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.24
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.45
 p-value of test no 179                :  7.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 183                :    0.36
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 186                :    0.91
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.40
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.42
 p-value of test no 196                :    0.49
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.20
 p-value of test no 198                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 200                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.04
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.28
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9987.53
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9865.54
 p-value of test no 215                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.72
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.55
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.45
 p-value of test no 218                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 221                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4747.80
 p-value of test no 222                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 225                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4768.06
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4139.98
 p-value of test no 227                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.19
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.75
 p-value of test no 229                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11676.00
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.85
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  8000027892
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.54
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999975995
 
 Normal statistic for number of bits   :   -0.19
 p-value of test no 234                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 238                :    0.60
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 242                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.54
 p-value of test no 244                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.60
 p-value of test no 248                :    0.94
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:33.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35876
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 10                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 11                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4246
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    2.48
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     973
 p-value of test no 25                 :  8.4e-3
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 27                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.48
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 32                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 36                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     272
 p-value of test no 37                 :    0.95
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 40                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 44                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.74
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.63
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.25
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.77
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.31
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.88
 p-value of test no 51                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.36
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.72
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.93
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.72
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.41
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7055.86
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 58                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.10
 p-value of test no 61                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 62                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 63                 :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   84.71
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.70
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  103.11
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5004.71
 p-value of test no 68                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45556
 p-value of test no 70                 :    0.93
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869556
   j =  1                              :        399908891
   j =  2                              :            45550
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45734
 p-value of test no 71                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869734
   j =  1                              :        399908536
   j =  2                              :            45726
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 73                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 74                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 78                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 80                 :  5.1e-3
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 83                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 85                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 88                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 94                 :  4.7e-3
 
 Anderson-Darling statistic = A2       :    5.65
 p-value of test no 95                 :  1.5e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 96                 :  5.2e-4    *****
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 98                 :  2.0e-3
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 102                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 103                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 105                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.19
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.66
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.88
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.56
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.92
 p-value of test no 122                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.17
 p-value of test no 123                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.29
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.56
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.52
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.74
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.77
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 136                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 137                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.56
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
 p-value of test no 142                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17848.68
 p-value of test no 145                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.65
 p-value of test no 146                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.87
 p-value of test no 147                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.65
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.10
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.05
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.34
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.12
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.57
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.46
 p-value of test no 155                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.83
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.53
 p-value of test no 157                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.65
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.41
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.06
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.91
 p-value of test no 161                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.92
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  490.45
 p-value of test no 163                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.30
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.89
 p-value of test no 165                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.69
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.84
 p-value of test no 167                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.47
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.62
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  155.08
 p-value of test no 170                :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.41
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.19
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5131.63
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.69
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.93
 p-value of test no 175                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.39
 p-value of test no 176                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.31
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.13
 p-value of test no 178                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 180                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 182                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 183                :    0.14
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
 p-value of test no 190                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
 p-value of test no 193                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 195                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.38
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.77
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.23
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.61
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 204                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 206                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.95
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 210                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10083.15
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.37
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.90
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.62
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4882.97
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4797.91
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.77
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.19
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11799.27
 p-value of test no 229                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.32
 p-value of test no 230                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.26
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000072877
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.64
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000037303
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 235                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 5.66e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    1.70
 p-value of test no 239                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.29
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 243                :    0.35
 
 Sample variance                       :    2.11
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.63
 p-value of test no 249                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 250                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:33.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  49  MaxOft, t = 32                  5.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35877
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 3                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 5                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 6                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 10                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5393
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4436
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7429
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4256
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7482
 p-value of test no 18                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7184
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 22                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    4.17
 p-value of test no 27                 :  7.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 30                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 33                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 34                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.48
 p-value of test no 35                 :    0.18
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 39                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 41                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    2.42
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.34
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.67
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.88
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.12
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.06
 p-value of test no 50                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.40
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.96
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.16
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  201.13
 p-value of test no 54                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.78
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.52
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7048.41
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.74
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 64                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.69
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.08
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.12
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4924.89
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45589
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869589
   j =  1                              :        399908826
   j =  2                              :            45581
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45800
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869800
   j =  1                              :        399908402
   j =  2                              :            45796
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 72                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 74                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 78                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 87                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
 p-value of test no 100                :    0.9970
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.23
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 104                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
 p-value of test no 109                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
 p-value of test no 110                :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 111                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 113                :    0.53
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 114                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 116                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 117                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.12
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.96
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.64
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.30
 p-value of test no 122                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.85
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.46
 p-value of test no 124                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.54
 p-value of test no 125                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.79
 p-value of test no 133                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.50
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.50
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17483.33
 p-value of test no 145                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.54
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.75
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.23
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.81
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.30
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.20
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.31
 p-value of test no 152                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.72
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.66
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.31
 p-value of test no 155                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.77
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.84
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.10
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.99
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.91
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.86
 p-value of test no 161                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.14
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.37
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.46
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.08
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.47
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.16
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.28
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  428.06
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  226.11
 p-value of test no 170                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.64
 p-value of test no 171                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.47
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.02
 p-value of test no 173                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.11
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.32
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.72
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.10
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.38
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 179                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 182                :    0.9918
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 186                :    0.06
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.04
 p-value of test no 188                :    0.02
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 195                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.15
 p-value of test no 196                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.79
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 201                :    0.30
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.16
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 206                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.61
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 208                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.19
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10080.70
 p-value of test no 215                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.085
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 217                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.57
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.32
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.49
 p-value of test no 227                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.16
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11836.24
 p-value of test no 229                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11908.02
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   29.89
 p-value of test no 231                :    0.9968
 
 
 -----------------------------------------------
 Total number of bits:  7999926831
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.75
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000029131
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 238                :    0.17
 
 Sample variance                       :    1.13
 p-value of test no 239                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.62
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.50
 p-value of test no 254                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:09.84
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35878
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 3                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 4                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 5                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 6                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 8                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1296
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334416
   j =  1                              :        599997408
   j =  2                              :             1296
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 11                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5578
 p-value of test no 13                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4221
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 18                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7190
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.37
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     942
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 26                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.22
 p-value of test no 28                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 29                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.93
 p-value of test no 32                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.56
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    2.19
 p-value of test no 36                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     339
 p-value of test no 37                 :    0.01
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 38                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 39                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.44
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 45                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.87
 p-value of test no 46                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.65
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.76
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.54
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.28
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.35
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.19
 p-value of test no 53                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  246.04
 p-value of test no 54                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  504.78
 p-value of test no 55                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.64
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7044.37
 p-value of test no 57                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 59                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 60                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.41
 p-value of test no 61                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.92
 p-value of test no 65                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.78
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.66
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4948.54
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908295
   j =  2                              :            45848
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46067
 p-value of test no 71                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870067
   j =  1                              :        399907867
   j =  2                              :            46065
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 74                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 76                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 90                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 95                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 103                :  4.5e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    5.62
 p-value of test no 105                :  1.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 107                :    0.90
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 3.36e-4
 p-value of test no 110                :    0.01
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
 p-value of test no 113                :    0.03
 
 Anderson-Darling statistic = A2       :    1.91
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : 8.10e-3
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 117                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   95.59
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.86
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.04
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.25
 p-value of test no 122                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.98
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.60
 p-value of test no 124                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.33
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 128                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.42
 p-value of test no 129                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.35
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.34
 p-value of test no 134                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 136                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.31
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.69
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.24
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.53
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.37
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.19
 p-value of test no 148                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.40
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.79
 p-value of test no 150                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.86
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.42
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.34
 p-value of test no 153                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.78
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.89
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.97
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.22
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.43
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.67
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.55
 p-value of test no 162                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.25
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.13
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.08
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.28
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.68
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5079.93
 p-value of test no 168                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.38
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.78
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.08
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.37
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5039.01
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.01
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.24
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.76
 p-value of test no 176                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.89
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 186                :    0.97
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.67
 p-value of test no 188                :    0.95
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.91
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.03
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.62
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.80
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 206                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.64
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 208                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.46
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.33
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 217                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 218                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.01
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 224                :    0.84
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4755.30
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.37
 p-value of test no 227                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.87
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.58
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11677.62
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  7999956381
 
 Normal statistic for number of bits   :   -0.34
 p-value of test no 232                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.05
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999996011
 
 Normal statistic for number of bits   :  -0.032
 p-value of test no 234                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 235                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 238                :    0.94
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 240                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 247                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 248                :    0.83
 
 Sample variance                       :    0.57
 p-value of test no 249                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 252                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 253                :    0.24
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:57.65
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35879
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 10                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 11                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5492
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4423
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 19                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 21                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 23                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.01
 p-value of test no 26                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.72
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 29                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 30                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     572
 p-value of test no 31                 :    0.87
 
 Stat. AD (mNP2)                       :    1.52
 p-value of test no 32                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 34                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    3.29
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 39                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.33
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    4.06
 p-value of test no 44                 :  8.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    2.40
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.49
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.12
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.66
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.68
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.51
 p-value of test no 51                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.82
 p-value of test no 52                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.64
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.66
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  424.75
 p-value of test no 55                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1498.35
 p-value of test no 56                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.16
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.54
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.40
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.69
 p-value of test no 66                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.89
 p-value of test no 67                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4957.47
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 70                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907955
   j =  2                              :            46018
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46014
 p-value of test no 71                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870014
   j =  1                              :        399907975
   j =  2                              :            46008
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 72                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 78                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.18
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 81                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 85                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.90
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 116                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.04
 p-value of test no 119                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.47
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.38
 p-value of test no 121                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.76
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.07
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.66
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.64
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.41
 p-value of test no 129                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.78
 p-value of test no 135                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.41
 p-value of test no 137                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  104.31
 p-value of test no 141                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.57
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17459.55
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.59
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.94
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.81
 p-value of test no 148                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.20
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.31
 p-value of test no 150                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.98
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.69
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.70
 p-value of test no 153                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.39
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.59
 p-value of test no 156                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.54
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  477.45
 p-value of test no 158                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.76
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.32
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.50
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.41
 p-value of test no 162                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  512.37
 p-value of test no 163                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.13
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.91
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.69
 p-value of test no 166                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.41
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.38
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.06
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.75
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.27
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.96
 p-value of test no 172                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4972.96
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.87
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.87
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.83
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.04
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.57
 p-value of test no 178                :    0.94
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.28
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 183                :    0.72
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 186                :    0.78
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 187                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 191                :    0.03
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 192                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.60
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.06
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 202                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.82
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.01
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.15
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 214                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.47
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 216                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 217                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4869.50
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 223                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4917.55
 p-value of test no 226                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.11
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.62
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11977.27
 p-value of test no 229                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11612.32
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.40
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000046684
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.66
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000036880
 
 Normal statistic for number of bits   :    0.29
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.24
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 238                :    0.37
 
 Sample variance                       :    0.38
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 243                :    0.28
 
 Sample variance                       :    1.59
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 246                :  3.6e-4    *****
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 247                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.09
 p-value of test no 248                :    0.02
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.95
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:49.31
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35880
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 3                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1197
 p-value of test no 11                 : 1 -  2.0e-6    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334317
   j =  1                              :        599997606
   j =  2                              :             1197
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 12                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5514
 p-value of test no 13                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4401
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 16                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4303
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7213
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     925
 p-value of test no 25                 :    0.21
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 30                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    0.20
 p-value of test no 42                 :    0.9901
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.11
 p-value of test no 46                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.01
 p-value of test no 47                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.21
 p-value of test no 48                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.50
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.31
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.09
 p-value of test no 51                 :    0.9948
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.34
 p-value of test no 52                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.33
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  225.35
 p-value of test no 54                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.65
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1436.16
 p-value of test no 56                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7058.63
 p-value of test no 57                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.42
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.81
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.45
 p-value of test no 66                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.44
 p-value of test no 67                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5157.85
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45604
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869604
   j =  1                              :        399908793
   j =  2                              :            45602
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45626
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869626
   j =  1                              :        399908749
   j =  2                              :            45624
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 93                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 95                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 102                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 106                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.85e-5
 p-value of test no 112                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
 p-value of test no 113                :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.38
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 116                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.38
 p-value of test no 119                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.74
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.07
 p-value of test no 121                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.73
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.24
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.54
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.44
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.27
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 132                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.44
 p-value of test no 133                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.33
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.33
 p-value of test no 135                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 136                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.14
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 142                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17528.88
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.67
 p-value of test no 146                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.53
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.13
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.51
 p-value of test no 149                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.79
 p-value of test no 150                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.26
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.21
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.78
 p-value of test no 153                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.95
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.72
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.74
 p-value of test no 156                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.63
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.49
 p-value of test no 158                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.79
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.60
 p-value of test no 160                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.80
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.36
 p-value of test no 162                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.97
 p-value of test no 163                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.53
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.95
 p-value of test no 165                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.82
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.50
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.69
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.95
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.68
 p-value of test no 170                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.90
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.73
 p-value of test no 172                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.91
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.91
 p-value of test no 174                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.61
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.38
 p-value of test no 176                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.38
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.37
 p-value of test no 178                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 183                :    0.32
 
 Sample variance                       :    2.14
 p-value of test no 184                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.15
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
 p-value of test no 191                :    0.60
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.35
 p-value of test no 196                :    0.31
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.63
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.18
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.21
 p-value of test no 203                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.31
 p-value of test no 207                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.34
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 210                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.65
 p-value of test no 211                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 214                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.20
 p-value of test no 215                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.10
 p-value of test no 216                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.06
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.68
 p-value of test no 222                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.18
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.79
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.34
 p-value of test no 228                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11932.41
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11627.10
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.33
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  7999977222
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.34
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999935942
 
 Normal statistic for number of bits   :   -0.51
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    1.24
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 243                :    0.63
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 253                :    0.75
 
 Sample variance                       :    1.26
 p-value of test no 254                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:49.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21          1 -  2.0e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35881
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 5                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 7                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 8                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 9                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 11                 :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5408
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 16                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 18                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7214
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.40
 p-value of test no 22                 :    0.06
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.78
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.84
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 26                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    2.05
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.91
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 33                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 36                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 41                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    2.55
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.05
 p-value of test no 46                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 48                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.93
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.91
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.42
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.83
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.13
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.35
 p-value of test no 54                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.75
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1478.35
 p-value of test no 56                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6948.57
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 58                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 60                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.36
 p-value of test no 61                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 64                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.92
 p-value of test no 65                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.31
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.30
 p-value of test no 67                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.51
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46311
 p-value of test no 70                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870311
   j =  1                              :        399907380
   j =  2                              :            46307
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46020
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870020
   j =  1                              :        399907962
   j =  2                              :            46016
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
 p-value of test no 72                 :    0.9925
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 76                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 87                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 88                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 95                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 98                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 102                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.08
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 109                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.00
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.14
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.93
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.59
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.74
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.25
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.39
 p-value of test no 125                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.80
 p-value of test no 129                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 132                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.21
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.17
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.97
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
 p-value of test no 138                :    0.9902
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.92
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17256.24
 p-value of test no 145                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.04
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   20.05
 p-value of test no 147                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.55
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.56
 p-value of test no 149                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.98
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.73
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.50
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.76
 p-value of test no 153                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.22
 p-value of test no 154                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.81
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.70
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.53
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.85
 p-value of test no 158                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.45
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.51
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.58
 p-value of test no 161                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.16
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.47
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.51
 p-value of test no 164                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.78
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  304.34
 p-value of test no 166                :    0.9990
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.47
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.31
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.77
 p-value of test no 169                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.69
 p-value of test no 170                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.89
 p-value of test no 171                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.05
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5082.25
 p-value of test no 173                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.90
 p-value of test no 174                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.94
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.78
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.08
 p-value of test no 177                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.20
 p-value of test no 178                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.060
 p-value of test no 179                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 182                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 183                :    0.82
 
 Sample variance                       :    2.08
 p-value of test no 184                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.21
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 195                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.63
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.03
 p-value of test no 198                :    0.43
 
 -----------------------------------------------
 Global longest run of 1               :   39.00
 p-value of test no 199                :  9.1e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 202                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.16
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.20
 p-value of test no 207                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 210                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9839.84
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 214                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.87
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 216                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.58
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4932.53
 p-value of test no 226                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.10
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4065.40
 p-value of test no 228                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11649.19
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.03
 p-value of test no 230                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.24
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000224149
 
 Normal statistic for number of bits   :    1.77
 p-value of test no 232                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.25
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000093397
 
 Normal statistic for number of bits   :    0.74
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 236                :  6.8e-3
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.86
 p-value of test no 238                :    0.03
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 242                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 247                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 248                :    0.08
 
 Sample variance                       :    0.92
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 253                :    0.84
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:36.39
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35882
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1452
 p-value of test no 4                  :  9.6e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334572
   j =  1                              :        599997096
   j =  2                              :             1452
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 5                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 6                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 7                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 8                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 10                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5480
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 18                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 20                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 21                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.66
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     879
 p-value of test no 25                 :    0.75
 
 Stat. AD (mNP2)                       :    1.61
 p-value of test no 26                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    2.43
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 28                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 29                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     631
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    3.01
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.81
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 35                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 39                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.32
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.56
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.91
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.63
 p-value of test no 50                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.45
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.26
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.01
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.28
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.86
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1517.35
 p-value of test no 56                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7110.25
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 60                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.78
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.11
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.10
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.08
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45812
 p-value of test no 70                 :    0.62
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869812
   j =  1                              :        399908381
   j =  2                              :            45802
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45846
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869846
   j =  1                              :        399908312
   j =  2                              :            45838
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 84                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 86                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 87                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.53
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 94                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 95                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.07
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 105                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 109                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 114                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.25
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.94
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.71
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.42
 p-value of test no 122                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.95
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.25
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.95
 p-value of test no 125                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.79
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.64
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.55
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.61
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.40
 p-value of test no 136                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 139                :    0.80
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.26
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17360.29
 p-value of test no 145                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.28
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.89
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.32
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.86
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.10
 p-value of test no 150                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.38
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.86
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.27
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.00
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.29
 p-value of test no 155                :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.57
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.76
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.42
 p-value of test no 158                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.87
 p-value of test no 159                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.10
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.05
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.69
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.46
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.11
 p-value of test no 164                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   91.38
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.36
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.08
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4919.96
 p-value of test no 168                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.44
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.58
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.56
 p-value of test no 171                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.84
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.56
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.54
 p-value of test no 174                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.94
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 176                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.19
 p-value of test no 177                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 178                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.89
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 188                :    0.29
 
 Sample variance                       :    1.35
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
 p-value of test no 190                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.13
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 192                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.76
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.51
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.86
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.27
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 210                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.86
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.07
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 216                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.35
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.11
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5000.10
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.09
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4171.79
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.81
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11925.57
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.08
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  7999977027
 
 Normal statistic for number of bits   :   -0.18
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.21
 p-value of test no 233                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999964718
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 241                :    0.98
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.58
 p-value of test no 243                :    0.94
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.18
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.32
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 251                :    0.94
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 253                :    0.79
 
 Sample variance                       :    1.19
 p-value of test no 254                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:24.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35883
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 3                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5357
 p-value of test no 13                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7501
 p-value of test no 19                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7219
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7090
 p-value of test no 21                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 23                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     943
 p-value of test no 25                 :    0.08
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.91
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 29                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 33                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 34                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 38                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    3.17
 p-value of test no 42                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     173
 p-value of test no 43                 :    0.04
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 44                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.31
 p-value of test no 46                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.05
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.70
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.29
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.83
 p-value of test no 50                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.09
 p-value of test no 51                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.57
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.70
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.23
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  446.55
 p-value of test no 55                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.76
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.10
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.80
 p-value of test no 61                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.41
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.19
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.25
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.47
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908083
   j =  2                              :            45951
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45689
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908623
   j =  2                              :            45687
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 74                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 76                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 78                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 80                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 86                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 95                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 103                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 105                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
 p-value of test no 109                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 111                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.11e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 114                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.78
 p-value of test no 115                :  2.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.082
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 117                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 118                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 119                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.84
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.88
 p-value of test no 121                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.98
 p-value of test no 122                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.83
 p-value of test no 123                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.20
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.77
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.55
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 132                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.22
 p-value of test no 133                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.96
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.57
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.52
 p-value of test no 141                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17488.47
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.36
 p-value of test no 146                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.16
 p-value of test no 147                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.53
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.69
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.53
 p-value of test no 150                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.89
 p-value of test no 151                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.27
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.28
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.26
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.87
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.91
 p-value of test no 156                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.25
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.98
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.61
 p-value of test no 159                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.22
 p-value of test no 160                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.58
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.48
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  474.59
 p-value of test no 163                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.68
 p-value of test no 164                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.26
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.61
 p-value of test no 166                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.00
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4825.39
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.92
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.80
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.56
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.45
 p-value of test no 172                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5095.16
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.28
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.21
 p-value of test no 176                :    0.95
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.038
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.91
 p-value of test no 184                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 186                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 187                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.59
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.95
 p-value of test no 189                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
 p-value of test no 190                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
 p-value of test no 194                :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 195                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.65
 p-value of test no 196                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.59
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 202                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.11
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.49
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 210                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10125.98
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10148.52
 p-value of test no 215                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.04
 p-value of test no 218                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 219                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.40
 p-value of test no 222                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4687.94
 p-value of test no 226                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4019.37
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.11
 p-value of test no 228                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11706.81
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11806.33
 p-value of test no 230                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.05
 p-value of test no 231                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  7999822959
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 232                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.09
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000058564
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.20
 p-value of test no 239                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 243                :    0.31
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 248                :    0.39
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.25
 p-value of test no 254                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:12.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35884
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 7                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 8                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5284
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 16                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 21                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 22                 :    0.9950
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 24                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.68
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.32
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 35                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    2.21
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.20
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 42                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    1.42
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    4.04
 p-value of test no 45                 :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.70
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.59
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.43
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.04
 p-value of test no 50                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.54
 p-value of test no 51                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.08
 p-value of test no 52                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.34
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.25
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.02
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1327.71
 p-value of test no 56                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7183.91
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.34
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 62                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 64                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   92.97
 p-value of test no 65                 :  4.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.03
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.09
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4890.54
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45584
 p-value of test no 70                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869584
   j =  1                              :        399908835
   j =  2                              :            45578
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45646
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869646
   j =  1                              :        399908710
   j =  2                              :            45642
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.25
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 81                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 84                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 87                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 88                 :    0.9983
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 90                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 94                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 106                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-5
 p-value of test no 109                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 111                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
 p-value of test no 112                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 114                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 115                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.36
 p-value of test no 116                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.058
 p-value of test no 117                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.29
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.54
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.36
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.69
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.73
 p-value of test no 123                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.60
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.44
 p-value of test no 125                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 128                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.95
 p-value of test no 129                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.58
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.22
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.80
 p-value of test no 135                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.62
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.45
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 144                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.24
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.75
 p-value of test no 146                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.75
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.23
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.55
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.00
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.43
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.17
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.66
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.13
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.43
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 157                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.20
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.74
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.49
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.18
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.41
 p-value of test no 162                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.47
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.06
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.32
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.87
 p-value of test no 166                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.19
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.84
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.94
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.44
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.43
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.25
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.24
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.65
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.09
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.43
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.12
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.65
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 182                :    0.9947
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.99
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.44
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
 p-value of test no 190                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.45
 p-value of test no 196                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.97
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.07
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 206                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.27
 p-value of test no 207                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.53
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 210                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9996.82
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.14
 p-value of test no 215                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.28
 p-value of test no 222                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9955
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4885.46
 p-value of test no 226                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.46
 p-value of test no 227                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.19
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.83
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11848.44
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.39
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000023803
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.76
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999940148
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 235                :  6.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 236                :    0.83
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 237                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.79
 p-value of test no 238                :    0.96
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.14
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 250                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:16.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35885
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 5                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 9                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 11                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 14                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4457
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4252
 p-value of test no 17                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 18                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 20                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.11
 p-value of test no 23                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 24                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 26                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 27                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 28                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 32                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 33                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.73
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    1.12
 p-value of test no 36                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    2.61
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.21
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.64
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.54
 p-value of test no 48                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.01
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.96
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.19
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.23
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.56
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.21
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.42
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.22
 p-value of test no 56                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6895.09
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.93
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 63                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.85
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.30
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4894.98
 p-value of test no 68                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45681
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869681
   j =  1                              :        399908639
   j =  2                              :            45679
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45547
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869547
   j =  1                              :        399908910
   j =  2                              :            45539
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 76                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
 p-value of test no 84                 :    0.9908
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 86                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 95                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 100                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 103                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
 p-value of test no 109                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
 p-value of test no 110                :    0.42
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 114                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.50
 p-value of test no 116                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.31
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.63
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.16
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.31
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.08
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.34
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.35
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.47
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.42
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.30
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.78
 p-value of test no 135                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.92
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 140                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.44
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.55
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.65
 p-value of test no 148                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.19
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.98
 p-value of test no 150                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.76
 p-value of test no 151                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.42
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.57
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.05
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.30
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.41
 p-value of test no 156                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.85
 p-value of test no 157                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  431.79
 p-value of test no 158                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.51
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.95
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.14
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.55
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.98
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.49
 p-value of test no 164                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.22
 p-value of test no 165                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.48
 p-value of test no 166                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.51
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5096.09
 p-value of test no 168                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.59
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.83
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.78
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.33
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5143.59
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.28
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.39
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.15
 p-value of test no 176                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 177                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 180                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.15
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 182                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 183                :    0.06
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.23
 p-value of test no 189                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.02
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.16
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 202                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.96
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 204                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.17
 p-value of test no 207                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9962.51
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10022.44
 p-value of test no 215                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 216                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.80
 p-value of test no 218                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 221                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.80
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 225                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4774.94
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4091.00
 p-value of test no 227                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.43
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11808.32
 p-value of test no 229                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11997.07
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.90
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999888071
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.99
 p-value of test no 233                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000044545
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 238                :    0.63
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 242                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 243                :    0.34
 
 Sample variance                       :    0.73
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 247                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 248                :    0.18
 
 Sample variance                       :    2.03
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 253                :    0.55
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35886
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 7                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 8                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 9                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 11                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5477
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4361
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 17                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7347
 p-value of test no 19                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 22                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     908
 p-value of test no 25                 :    0.40
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 33                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.35
 p-value of test no 38                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 42                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 45                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.16
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.25
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.13
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.90
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.20
 p-value of test no 50                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.35
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.86
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.77
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.52
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.97
 p-value of test no 55                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1407.31
 p-value of test no 56                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7156.64
 p-value of test no 57                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.92
 p-value of test no 61                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 63                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.96
 p-value of test no 65                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.06
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.02
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5154.40
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908032
   j =  2                              :            45978
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45844
 p-value of test no 71                 :    0.56
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869844
   j =  1                              :        399908315
   j =  2                              :            45838
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 72                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 74                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 81                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 93                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 99                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 102                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 107                :    0.80
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 111                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 115                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 116                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.45
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.31
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.10
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.52
 p-value of test no 120                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.97
 p-value of test no 121                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.82
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.26
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.52
 p-value of test no 124                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.17
 p-value of test no 125                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.75
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.18
 p-value of test no 129                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.97
 p-value of test no 133                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.09
 p-value of test no 135                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   10.28
 p-value of test no 137                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.10
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17629.68
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.55
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.99
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.10
 p-value of test no 149                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.46
 p-value of test no 151                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.23
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.51
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.82
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.99
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.47
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.27
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.47
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.26
 p-value of test no 159                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.15
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.37
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.58
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.89
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.59
 p-value of test no 164                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.14
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.91
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.77
 p-value of test no 167                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.77
 p-value of test no 168                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.18
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.64
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.15
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.52
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.00
 p-value of test no 173                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  401.41
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.32
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.26
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.53
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.80
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 187                :    0.9939
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.25
 p-value of test no 188                :    0.60
 
 Sample variance                       :    0.76
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
 p-value of test no 190                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.72
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.18
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.60
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.86
 p-value of test no 203                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.85
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 209                :    0.88
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.36
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9831.37
 p-value of test no 215                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 219                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 220                :    0.14
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5003.99
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4927.86
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4223.94
 p-value of test no 227                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4222.38
 p-value of test no 228                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12094.25
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.71
 p-value of test no 230                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.02
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  8000024610
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.52
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000101146
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.49
 p-value of test no 239                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.27
 p-value of test no 244                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.60
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:45.37
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35887
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 12                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5497
 p-value of test no 13                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 15                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.22
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 28                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.63
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 34                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.78
 p-value of test no 36                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 39                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 40                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.45
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.21
 p-value of test no 44                 :    0.99
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.15
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.32
 p-value of test no 47                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.78
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.91
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   36.03
 p-value of test no 50                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.09
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.83
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.25
 p-value of test no 53                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.77
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  471.24
 p-value of test no 55                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1434.46
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7021.90
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 60                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.15
 p-value of test no 61                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 64                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.61
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.98
 p-value of test no 66                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.67
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.21
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46049
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870049
   j =  1                              :        399907909
   j =  2                              :            46035
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46204
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870204
   j =  1                              :        399907597
   j =  2                              :            46194
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 72                 :    0.9955
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 73                 :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.08
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  8.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 81                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 86                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 87                 :  7.5e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 88                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  5.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 102                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 103                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.81e-4
 p-value of test no 112                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
 p-value of test no 113                :    0.75
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 115                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.050
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.40
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.32
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.25
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.66
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.71
 p-value of test no 123                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.25
 p-value of test no 124                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.69
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.32
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.30
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.25
 p-value of test no 133                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.97
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.00
 p-value of test no 135                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 136                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.23
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17286.22
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.72
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.49
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.62
 p-value of test no 148                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.21
 p-value of test no 149                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.28
 p-value of test no 150                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.81
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.79
 p-value of test no 152                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.83
 p-value of test no 153                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.37
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.18
 p-value of test no 155                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.73
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.42
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.49
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.64
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.96
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.50
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.21
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.49
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.26
 p-value of test no 164                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.94
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.16
 p-value of test no 166                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 167                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.01
 p-value of test no 168                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.74
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.51
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.44
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.72
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5104.24
 p-value of test no 173                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.43
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.92
 p-value of test no 175                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.65
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.63
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.44
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 181                :    0.01
 
 Anderson-Darling statistic = A2       :    2.77
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.16
 p-value of test no 183                :    0.02
 
 Sample variance                       :    0.93
 p-value of test no 184                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.54
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.21
 p-value of test no 196                :    0.62
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.52
 p-value of test no 198                :    0.90
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.31
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.45
 p-value of test no 207                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 208                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10128.99
 p-value of test no 211                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10017.68
 p-value of test no 215                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.03
 p-value of test no 217                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 221                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4952.46
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4935.26
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4104.96
 p-value of test no 227                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4174.12
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11663.94
 p-value of test no 229                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.94
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.75
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000054874
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.68
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999983942
 
 Normal statistic for number of bits   :   -0.13
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 242                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 243                :    0.59
 
 Sample variance                       :    0.34
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 247                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 248                :    0.41
 
 Sample variance                       :    1.41
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    2.49
 p-value of test no 252                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.22
 p-value of test no 253                :    0.01
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:28.95
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35888
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 6                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 7                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1479
 p-value of test no 9                  :  1.1e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334599
   j =  1                              :        599997042
   j =  2                              :             1479
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 12                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5425
 p-value of test no 13                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 14                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 16                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7353
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7154
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 20                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 22                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    1.56
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.86
 p-value of test no 30                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    2.10
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 34                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     323
 p-value of test no 37                 :    0.10
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.11
 p-value of test no 46                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.85
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.81
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.85
 p-value of test no 49                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.53
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.73
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.46
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.67
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  276.63
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.33
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.20
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6959.00
 p-value of test no 57                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 59                 :    0.09
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.39
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 62                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.91
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.08
 p-value of test no 66                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.11
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4943.90
 p-value of test no 68                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45523
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869523
   j =  1                              :        399908957
   j =  2                              :            45517
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45785
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869785
   j =  1                              :        399908433
   j =  2                              :            45779
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 80                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 84                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 85                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 91                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.40
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 95                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 98                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 102                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.59
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.51e-5
 p-value of test no 110                :    0.9909
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.41e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    3.54
 p-value of test no 114                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.088
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.70
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.58
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.53
 p-value of test no 121                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.94
 p-value of test no 122                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.94
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.70
 p-value of test no 124                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   48.88
 p-value of test no 125                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.40
 p-value of test no 129                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.97
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.50
 p-value of test no 133                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.69
 p-value of test no 134                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.98
 p-value of test no 135                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 140                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.66
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17657.43
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.72
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.64
 p-value of test no 147                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.74
 p-value of test no 148                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.24
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.94
 p-value of test no 150                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.26
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.20
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.76
 p-value of test no 153                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.06
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.66
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.59
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 157                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.64
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.64
 p-value of test no 159                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.76
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.48
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.38
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.77
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.63
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.68
 p-value of test no 165                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  438.35
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.91
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.84
 p-value of test no 168                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.06
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.12
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.57
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.89
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5175.29
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.76
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.63
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.31
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.033
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.06
 p-value of test no 178                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 182                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.07e-3
 p-value of test no 185                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 186                :    0.04
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.06
 p-value of test no 188                :    0.02
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
 p-value of test no 190                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 191                :    0.58
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.66
 p-value of test no 196                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.33
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 202                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.70
 p-value of test no 203                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.36
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.86
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 208                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 210                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9764.48
 p-value of test no 211                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9723.78
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 217                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.72
 p-value of test no 222                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 223                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.71
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.37
 p-value of test no 226                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.98
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.67
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.96
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.01
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.41
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999898310
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 232                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.54
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000175249
 
 Normal statistic for number of bits   :    1.39
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 238                :    0.16
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.80
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 248                :    0.67
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.042
 p-value of test no 253                :    0.48
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:53.89
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35889
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1448
 p-value of test no 3                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334568
   j =  1                              :        599997104
   j =  2                              :             1448
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 5                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 7                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 11                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1282
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334402
   j =  1                              :        599997436
   j =  2                              :             1282
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5345
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 18                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 19                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 20                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 21                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.24
 p-value of test no 26                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 29                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    4.49
 p-value of test no 30                 :  5.1e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     552
 p-value of test no 31                 :    0.97
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.88
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 34                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     285
 p-value of test no 37                 :    0.80
 
 Stat. AD (mNP2)                       :    1.68
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 39                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.24
 p-value of test no 41                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.20
 p-value of test no 44                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    1.73
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.68
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.84
 p-value of test no 47                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.12
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.64
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.19
 p-value of test no 50                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.46
 p-value of test no 51                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.56
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.59
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.08
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.91
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.48
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7063.36
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.27
 p-value of test no 61                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 64                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.07
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   20.89
 p-value of test no 66                 :  8.5e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.86
 p-value of test no 67                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.87
 p-value of test no 68                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46542
 p-value of test no 70                 :  1.0e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870542
   j =  1                              :        399906920
   j =  2                              :            46534
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46130
 p-value of test no 71                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870130
   j =  1                              :        399907745
   j =  2                              :            46120
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 72                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 74                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 78                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 84                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 85                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 87                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 93                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 95                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.62
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 102                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.45
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 105                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 106                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
 p-value of test no 112                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.45
 p-value of test no 116                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.17
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.90
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.10
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.68
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.88
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.18
 p-value of test no 122                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.42
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.36
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.42
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.78
 p-value of test no 129                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.59
 p-value of test no 133                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  : 7.01e-3
 p-value of test no 135                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.61
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 142                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17297.34
 p-value of test no 145                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.81
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.70
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.84
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.80
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.83
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.54
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.64
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.51
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.82
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.42
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.30
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.50
 p-value of test no 157                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.00
 p-value of test no 158                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.46
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.67
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  184.88
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.88
 p-value of test no 162                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.02
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.06
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.82
 p-value of test no 165                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.60
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.62
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5108.26
 p-value of test no 168                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.72
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  220.65
 p-value of test no 170                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.06
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.45
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4973.93
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.42
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.49
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.56
 p-value of test no 176                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.09
 p-value of test no 178                :    0.61
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 180                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
 p-value of test no 194                :    0.73
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.36
 p-value of test no 196                :    0.72
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.16
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.34
 p-value of test no 203                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.43
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 206                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.20
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9951.91
 p-value of test no 211                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.89
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.17
 p-value of test no 217                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.60
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.25
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4005.32
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4002.11
 p-value of test no 228                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11900.44
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11669.47
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.75
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000021118
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.06
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  7999851843
 
 Normal statistic for number of bits   :   -1.17
 p-value of test no 234                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.093
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 239                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 242                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.87
 p-value of test no 248                :    0.81
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.75
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              8.5e-4
  69  MatrixRank, L=1000, r=26        0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35890
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 3                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 5                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 6                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 10                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 12                 :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5385
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4335
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 15                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4347
 p-value of test no 17                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 21                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.46
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    2.07
 p-value of test no 24                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     890
 p-value of test no 25                 :    0.62
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 27                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 28                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 32                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.93
 p-value of test no 34                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 38                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.78
 p-value of test no 40                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    2.03
 p-value of test no 44                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.04
 p-value of test no 46                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.94
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.87
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.05
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.99
 p-value of test no 50                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.72
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.45
 p-value of test no 52                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.14
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.98
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  409.52
 p-value of test no 55                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.06
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6961.78
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.94
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.34
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.72
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  142.01
 p-value of test no 67                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.68
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45792
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869792
   j =  1                              :        399908422
   j =  2                              :            45780
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908666
   j =  2                              :            45655
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 76                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 95                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 98                 :    0.9910
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 100                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 102                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 105                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
 p-value of test no 109                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 114                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.02
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.52
 p-value of test no 117                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 118                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.04
 p-value of test no 119                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.86
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.33
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.33
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.43
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.36
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 128                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.09
 p-value of test no 129                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.70
 p-value of test no 133                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.23
 p-value of test no 134                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.10
 p-value of test no 135                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.47
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 138                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.75
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 144                :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17421.04
 p-value of test no 145                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.32
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   12.71
 p-value of test no 147                :    0.9998    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.18
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.03
 p-value of test no 149                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.25
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.17
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.40
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.06
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.46
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.54
 p-value of test no 155                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.22
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.36
 p-value of test no 157                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.69
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.99
 p-value of test no 159                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.28
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.72
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.79
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.86
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.37
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.42
 p-value of test no 166                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.18
 p-value of test no 167                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4848.03
 p-value of test no 168                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.63
 p-value of test no 169                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  167.23
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.48
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.97
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4840.68
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.23
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.70
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   26.44
 p-value of test no 176                :  9.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.17
 p-value of test no 177                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.53
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.51
 p-value of test no 183                :    0.07
 
 Sample variance                       :    1.81
 p-value of test no 184                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 187                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.50
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 192                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.95
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.93
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 201                :    0.89
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 202                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  184.17
 p-value of test no 203                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 205                :    0.03
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 206                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  238.16
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.42
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.57
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.72
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 216                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 220                :    0.93
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4732.62
 p-value of test no 222                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5049.44
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.16
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.09
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.89
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11858.54
 p-value of test no 230                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.66
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999892217
 
 Normal statistic for number of bits   :   -0.85
 p-value of test no 232                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.94
 p-value of test no 233                :    0.77
 
 
 -----------------------------------------------
 Total number of bits:  8000011527
 
 Normal statistic for number of bits   :   0.091
 p-value of test no 234                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 236                :    0.07
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 237                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.37
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.31
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 242                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 244                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.49
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 247                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 248                :    0.20
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    0.31
 p-value of test no 254                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.25
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 M (L=50, r=0)       0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35891
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 10                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 12                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5394
 p-value of test no 13                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4281
 p-value of test no 17                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 18                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 20                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 24                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    2.16
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.01
 p-value of test no 29                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 30                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 32                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 33                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.35
 p-value of test no 34                 :    0.22
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    1.60
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.93
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 44                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.88
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.73
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.80
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.99
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.96
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  447.56
 p-value of test no 55                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1422.01
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7075.42
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.08
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.23
 p-value of test no 65                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.83
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.86
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5028.32
 p-value of test no 68                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45822
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869822
   j =  1                              :        399908359
   j =  2                              :            45816
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907844
   j =  2                              :            46072
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 72                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 97                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 99                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 104                :    0.77
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 111                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 114                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.048
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 118                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.49
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   41.59
 p-value of test no 120                :    0.9937
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.90
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.64
 p-value of test no 122                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   63.37
 p-value of test no 123                :  4.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.39
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.85
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 128                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.50
 p-value of test no 129                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.42
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 134                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.32
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17271.73
 p-value of test no 145                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.51
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.89
 p-value of test no 147                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.92
 p-value of test no 148                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.03
 p-value of test no 149                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.75
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.07
 p-value of test no 151                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.75
 p-value of test no 152                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.47
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.68
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.15
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.41
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.57
 p-value of test no 157                :  4.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.27
 p-value of test no 158                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.74
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.07
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.77
 p-value of test no 161                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.00
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.73
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.51
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   50.67
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.44
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.80
 p-value of test no 167                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.54
 p-value of test no 168                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.44
 p-value of test no 169                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.17
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.81
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.91
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4929.37
 p-value of test no 173                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.15
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  228.06
 p-value of test no 175                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.55
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.35
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    2.59
 p-value of test no 178                :    0.9978
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 179                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 183                :    0.40
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 187                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 195                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.45
 p-value of test no 196                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.13
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
 p-value of test no 201                :    0.9989
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 202                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  157.07
 p-value of test no 203                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 206                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.38
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10068.97
 p-value of test no 211                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.69
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 216                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.01
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4838.80
 p-value of test no 222                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 225                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.65
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3981.84
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4170.72
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11761.23
 p-value of test no 229                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11603.28
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.00
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999989843
 
 Normal statistic for number of bits   :  -0.080
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.64
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  8000064621
 
 Normal statistic for number of bits   :    0.51
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 238                :    0.34
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.55
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 242                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 243                :    0.41
 
 Sample variance                       :    1.28
 p-value of test no 244                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 246                :    0.87
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    1.19
 p-value of test no 249                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 250                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 251                :    0.07
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 252                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.85
 p-value of test no 253                :    0.03
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:49.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35892
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 3                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 5                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 6                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 10                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5538
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7243
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 19                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     926
 p-value of test no 25                 :    0.20
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 26                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 28                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     624
 p-value of test no 31                 :    0.17
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 33                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    2.13
 p-value of test no 36                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     268
 p-value of test no 37                 :    0.97
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 40                 :    0.73
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 42                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     139
 p-value of test no 43                 :    0.80
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.84
 p-value of test no 46                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.88
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.83
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.10
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.14
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   77.41
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.40
 p-value of test no 53                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  233.99
 p-value of test no 54                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.54
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1452.15
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6873.90
 p-value of test no 57                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 59                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.39
 p-value of test no 61                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 64                 :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.68
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.16
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.78
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4899.80
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46034
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870034
   j =  1                              :        399907937
   j =  2                              :            46024
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45920
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869920
   j =  1                              :        399908164
   j =  2                              :            45912
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 78                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 79                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 80                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.13
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 92                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 95                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    3.16
 p-value of test no 102                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 104                :    0.13
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 108                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
 p-value of test no 109                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 110                :    0.15
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
 p-value of test no 112                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 118                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.38
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.56
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.68
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.76
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.01
 p-value of test no 123                :    0.9980
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.85
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.65
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
 p-value of test no 126                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   54.84
 p-value of test no 129                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.94
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.29
 p-value of test no 135                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.65
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.15
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17412.80
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.90
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   56.06
 p-value of test no 147                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.41
 p-value of test no 148                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.30
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.71
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.08
 p-value of test no 151                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.65
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.05
 p-value of test no 153                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.51
 p-value of test no 154                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.40
 p-value of test no 155                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.11
 p-value of test no 156                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 157                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  517.14
 p-value of test no 158                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.22
 p-value of test no 159                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.66
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.48
 p-value of test no 161                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.85
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.44
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.76
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.57
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.03
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.98
 p-value of test no 167                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4989.41
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.75
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.49
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.28
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.10
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  402.29
 p-value of test no 174                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.96
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.63
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.50
 p-value of test no 177                :    0.9938
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.61
 p-value of test no 178                :    0.97
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 179                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
 p-value of test no 193                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.82
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.63
 p-value of test no 203                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 204                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 205                :    0.94
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.34
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 210                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10065.61
 p-value of test no 211                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.65
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.65
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.20
 p-value of test no 217                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.98
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.62
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 225                :    0.9942
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.91
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4215.05
 p-value of test no 227                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.09
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.05
 p-value of test no 229                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.94
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.77
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000131893
 
 Normal statistic for number of bits   :    1.04
 p-value of test no 232                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.44
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000166783
 
 Normal statistic for number of bits   :    1.32
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 237                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 238                :    0.54
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    1.81
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.31
 p-value of test no 248                :    0.91
 
 Sample variance                       :    1.35
 p-value of test no 249                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 251                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.94
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35893
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 5                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 7                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 9                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 12                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4259
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 17                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 18                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 21                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.82
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     917
 p-value of test no 25                 :    0.29
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 27                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 29                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.03
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.40
 p-value of test no 38                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 40                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 41                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 45                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.74
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.71
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.45
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.64
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.45
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.82
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.82
 p-value of test no 54                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.42
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.18
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7309.81
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.49
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.33
 p-value of test no 65                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.96
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.41
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4964.44
 p-value of test no 68                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46416
 p-value of test no 70                 :  6.2e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870416
   j =  1                              :        399907172
   j =  2                              :            46408
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908211
   j =  2                              :            45884
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 72                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 81                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 83                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 84                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 85                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 99                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 105                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
 p-value of test no 109                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.01e-5
 p-value of test no 113                :    0.94
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 115                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 117                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.14
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.28
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.91
 p-value of test no 121                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.87
 p-value of test no 122                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.75
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.68
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   46.67
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.10
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 132                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.92
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.60
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 137                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.38
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  126.10
 p-value of test no 141                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 143                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17571.15
 p-value of test no 145                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.71
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.41
 p-value of test no 147                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.94
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.08
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.60
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.18
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.24
 p-value of test no 152                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.89
 p-value of test no 153                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.80
 p-value of test no 154                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   31.05
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.60
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  174.80
 p-value of test no 157                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  452.06
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.89
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.36
 p-value of test no 160                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.52
 p-value of test no 161                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.28
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.46
 p-value of test no 163                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.22
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.59
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.64
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.36
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.72
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.68
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.53
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.12
 p-value of test no 171                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.93
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4858.75
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.88
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.15
 p-value of test no 175                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.43
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.25
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 182                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.15
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 187                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.83
 p-value of test no 188                :    0.20
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.23
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.16e-3
 p-value of test no 193                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 194                :    0.03
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.55
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.22
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  190.78
 p-value of test no 203                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.27
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.51
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 212                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10079.86
 p-value of test no 215                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.081
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 217                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 220                :    0.29
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.48
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 223                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.76
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.47
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4261.36
 p-value of test no 228                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11691.40
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11866.37
 p-value of test no 230                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.23
 p-value of test no 231                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  8000015136
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.03
 p-value of test no 233                :    0.51
 
 
 -----------------------------------------------
 Total number of bits:  8000026230
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 236                :    0.82
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    0.82
 p-value of test no 239                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.60
 p-value of test no 244                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 247                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 250                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    0.72
 p-value of test no 254                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:28.03
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35894
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 4                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 8                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 9                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1238
 p-value of test no 11                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334358
   j =  1                              :        599997524
   j =  2                              :             1238
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 14                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7351
 p-value of test no 18                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7487
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7157
 p-value of test no 20                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 21                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 24                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 27                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.76
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 36                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 38                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 42                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 44                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.84
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.35
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.03
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.23
 p-value of test no 50                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.05
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.51
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.20
 p-value of test no 53                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.45
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.62
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.06
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7071.18
 p-value of test no 57                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.72
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.83
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.84
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.07
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.33
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46100
 p-value of test no 70                 :    0.15
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870100
   j =  1                              :        399907805
   j =  2                              :            46090
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45453
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869453
   j =  1                              :        399909099
   j =  2                              :            45443
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 74                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 85                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 88                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 105                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 106                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 109                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.48e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
 p-value of test no 113                :    0.91
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 114                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.07
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.75
 p-value of test no 119                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.04
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.11
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.38
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.66
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.84
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.33
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 126                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 128                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.41
 p-value of test no 129                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.75
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.40
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.09
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.70
 p-value of test no 136                :  1.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 137                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  120.38
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 142                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    3.77
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16961.88
 p-value of test no 145                :    0.9942
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.24
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.95
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.70
 p-value of test no 148                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.04
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.47
 p-value of test no 150                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.77
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.69
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.24
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.44
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.81
 p-value of test no 155                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.09
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.51
 p-value of test no 157                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  510.29
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.89
 p-value of test no 159                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.67
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  108.63
 p-value of test no 161                :    0.9910
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.89
 p-value of test no 162                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  524.30
 p-value of test no 163                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.25
 p-value of test no 164                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.64
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  324.60
 p-value of test no 166                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.02
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5077.80
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  328.47
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.54
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.57
 p-value of test no 171                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.51
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4896.42
 p-value of test no 173                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.08
 p-value of test no 174                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.86
 p-value of test no 175                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.39
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.34
 p-value of test no 177                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.03
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.89
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.69
 p-value of test no 184                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.51
 p-value of test no 188                :    0.31
 
 Sample variance                       :    2.45
 p-value of test no 189                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 198                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.45
 p-value of test no 203                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.07
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10103.79
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.60
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.58
 p-value of test no 216                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 217                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.51
 p-value of test no 218                :    0.9998    *****
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4893.14
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5027.74
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.96
 p-value of test no 227                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.36
 p-value of test no 228                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11826.69
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11981.26
 p-value of test no 230                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.93
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000082909
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.60
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000003784
 
 Normal statistic for number of bits   :   0.030
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.57
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 240                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 243                :    0.37
 
 Sample variance                       :    1.48
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.70
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.26
 p-value of test no 249                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 250                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.45
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 252                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 9.82e-3
 p-value of test no 253                :    0.50
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:01.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9997 
  94  HammingCorr, L = 1200           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35895
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1255
 p-value of test no 3                  :    0.9986
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334375
   j =  1                              :        599997490
   j =  2                              :             1255
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 10                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5386
 p-value of test no 13                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 15                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4321
 p-value of test no 16                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 17                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7210
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7380
 p-value of test no 19                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7188
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 23                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     857
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 30                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 38                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 39                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 40                 :    0.98
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.53
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 45                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.66
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.20
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.64
 p-value of test no 48                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.16
 p-value of test no 49                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.14
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.99
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.37
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.82
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  194.18
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.21
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.76
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6972.48
 p-value of test no 57                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 59                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.35
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.35
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.89
 p-value of test no 66                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.81
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5057.36
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45828
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869828
   j =  1                              :        399908351
   j =  2                              :            45814
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46027
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870027
   j =  1                              :        399907950
   j =  2                              :            46019
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 76                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 78                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 81                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 83                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 91                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 94                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 95                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 99                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 103                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 105                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 107                :    0.02
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 108                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
 p-value of test no 109                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
 p-value of test no 113                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.28
 p-value of test no 116                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 117                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 118                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.47
 p-value of test no 119                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.98
 p-value of test no 120                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.30
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.38
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.94
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.32
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.91
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 128                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.45
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 130                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.55
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.90
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.25
 p-value of test no 135                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 140                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.92
 p-value of test no 141                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 142                :    0.9928
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.34
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17669.00
 p-value of test no 145                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.44
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.67
 p-value of test no 147                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.25
 p-value of test no 148                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.22
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.75
 p-value of test no 150                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.49
 p-value of test no 151                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.50
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.66
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.40
 p-value of test no 155                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.51
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  480.63
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.20
 p-value of test no 159                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.79
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.91
 p-value of test no 161                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.68
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  506.56
 p-value of test no 163                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.84
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.78
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  306.91
 p-value of test no 167                :    0.9985
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.84
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.77
 p-value of test no 169                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.59
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.23
 p-value of test no 171                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.05
 p-value of test no 172                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.89
 p-value of test no 173                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.08
 p-value of test no 174                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.54
 p-value of test no 175                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.66
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.92
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.58
 p-value of test no 178                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.052
 p-value of test no 179                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.52
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    1.08
 p-value of test no 184                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 188                :    0.75
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.84
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.03
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 202                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  163.90
 p-value of test no 203                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 204                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 205                :    0.95
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  170.24
 p-value of test no 207                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.42
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 212                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 213                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 214                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10117.03
 p-value of test no 215                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.68
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.18
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4966.90
 p-value of test no 226                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4189.01
 p-value of test no 227                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3963.32
 p-value of test no 228                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11828.38
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11840.61
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.00
 p-value of test no 231                :    0.36
 
 
 -----------------------------------------------
 Total number of bits:  7999829538
 
 Normal statistic for number of bits   :   -1.35
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.84
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999900035
 
 Normal statistic for number of bits   :   -0.79
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 237                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 241                :  3.2e-4    *****
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 242                :  3.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.62
 p-value of test no 243                :  4.3e-3
 
 Sample variance                       :    0.23
 p-value of test no 244                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.88
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.96
 p-value of test no 254                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:14.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35896
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 5                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 6                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 11                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1278
 p-value of test no 12                 :    0.9904
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334398
   j =  1                              :        599997444
   j =  2                              :             1278
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5485
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4310
 p-value of test no 14                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 17                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 19                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7424
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.15
 p-value of test no 23                 :    0.9985
 
 Test on the Nm values of W_{n,i}(mNP1):    2.74
 p-value of test no 24                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 27                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 28                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.12
 p-value of test no 35                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.66
 p-value of test no 36                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    1.10
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 40                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 41                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.33
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.92
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.59
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.84
 p-value of test no 48                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.10
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.43
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.39
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.99
 p-value of test no 53                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.37
 p-value of test no 54                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.39
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1402.32
 p-value of test no 56                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6827.85
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 58                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.06
 p-value of test no 61                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 63                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.03
 p-value of test no 65                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.89
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.31
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5042.64
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908284
   j =  2                              :            45849
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 71                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908121
   j =  2                              :            45935
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 72                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 76                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 78                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 85                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 86                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 95                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 98                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 99                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.24
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 108                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 111                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 112                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 114                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 115                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.89
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.40
 p-value of test no 119                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.58
 p-value of test no 120                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.67
 p-value of test no 121                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.01
 p-value of test no 122                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.43
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.82
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.26
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.20
 p-value of test no 129                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.30
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.28
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.11
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 140                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.96
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 143                :    0.97
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17225.79
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   20.08
 p-value of test no 146                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   19.23
 p-value of test no 147                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.85
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.35
 p-value of test no 149                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.22
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.76
 p-value of test no 151                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.91
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.70
 p-value of test no 153                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.61
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.24
 p-value of test no 155                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.25
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.40
 p-value of test no 157                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.46
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.59
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.58
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.26
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.23
 p-value of test no 162                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.15
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.67
 p-value of test no 164                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.03
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.26
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.99
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4904.12
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.31
 p-value of test no 169                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.01
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.48
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.51
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5112.93
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.78
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  171.33
 p-value of test no 175                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.92
 p-value of test no 176                :    0.54
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.019
 p-value of test no 177                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.05
 p-value of test no 178                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.037
 p-value of test no 179                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 183                :    0.09
 
 Sample variance                       :    0.70
 p-value of test no 184                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.40
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.86
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
 p-value of test no 191                :    0.63
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
 p-value of test no 193                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 195                :    0.9941
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.31
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.14
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 199                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.07
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.55
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 210                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9735.97
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9916.87
 p-value of test no 215                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4819.23
 p-value of test no 222                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 225                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.38
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.29
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.30
 p-value of test no 228                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11903.48
 p-value of test no 229                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.94
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.67
 p-value of test no 231                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999871643
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.56
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  8000028315
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 235                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.71
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 237                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 238                :    0.91
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 240                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 248                :    0.19
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.67
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    1.33
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:25.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35897
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 3                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 4                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 5                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 9                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5489
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4334
 p-value of test no 14                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 15                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4365
 p-value of test no 16                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4312
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 21                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    1.68
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 38                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.87
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 41                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     133
 p-value of test no 43                 :    0.91
 
 Stat. AD (mNP2)                       :    3.63
 p-value of test no 44                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 45                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.36
 p-value of test no 46                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.79
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.00
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.36
 p-value of test no 49                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.45
 p-value of test no 50                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.96
 p-value of test no 51                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.91
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.16
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.38
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.02
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1418.28
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.15
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.77
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.14
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.63
 p-value of test no 66                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   84.47
 p-value of test no 67                 :    0.9930
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.77
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9911
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45544
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869544
   j =  1                              :        399908914
   j =  2                              :            45540
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908053
   j =  2                              :            45969
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 86                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 88                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 91                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 93                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 101                :    0.89
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
 p-value of test no 109                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 111                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
 p-value of test no 112                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 114                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.021
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 117                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 118                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.94
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.29
 p-value of test no 120                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.20
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.18
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.36
 p-value of test no 124                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.90
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 127                :    0.21
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 128                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.83
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 132                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.08
 p-value of test no 133                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.61
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.078
 p-value of test no 135                :    0.9943
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.06
 p-value of test no 136                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.16
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 139                :    0.07
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 140                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.27
 p-value of test no 141                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.56
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17334.82
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.46
 p-value of test no 147                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.12
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.34
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.84
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.27
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.00
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.69
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.59
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.48
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.05
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.08
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.52
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.19
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.54
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.66
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.00
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.70
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.52
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.99
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.35
 p-value of test no 166                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.87
 p-value of test no 167                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4931.08
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.23
 p-value of test no 169                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.30
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.06
 p-value of test no 171                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.73
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5032.10
 p-value of test no 173                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.67
 p-value of test no 174                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.99
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.07
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.63
 p-value of test no 177                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.86
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.021
 p-value of test no 179                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 183                :    0.28
 
 Sample variance                       :    0.82
 p-value of test no 184                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.03
 p-value of test no 188                :    0.85
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 9.09e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.63
 p-value of test no 196                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.93
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
 p-value of test no 200                :    0.9977
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  262.93
 p-value of test no 203                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 206                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.71
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 210                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10149.49
 p-value of test no 211                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 214                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9925.17
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.54
 p-value of test no 217                :  5.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 218                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.40
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.17
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.99
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.72
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3986.91
 p-value of test no 228                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.08
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.16
 p-value of test no 230                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.32
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000107131
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.54
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999933656
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 242                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 253                :    0.88
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:16.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35898
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 3                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 4                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 6                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 10                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1257
 p-value of test no 12                 :    0.9983
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334377
   j =  1                              :        599997486
   j =  2                              :             1257
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5392
 p-value of test no 13                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 16                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7571
 p-value of test no 19                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 21                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 22                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 23                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    3.34
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     845
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.95
 p-value of test no 29                 :  9.4e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     626
 p-value of test no 31                 :    0.15
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    6.93
 p-value of test no 34                 :  3.9e-4    *****
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    2.06
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    2.20
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 40                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 44                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 45                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.83
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.16
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.19
 p-value of test no 48                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.39
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.04
 p-value of test no 51                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.13
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.99
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.86
 p-value of test no 54                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.42
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1427.09
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.38
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 60                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.18
 p-value of test no 61                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.03
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.11
 p-value of test no 66                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.52
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5049.33
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907972
   j =  2                              :            46011
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46043
 p-value of test no 71                 :    0.22
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870043
   j =  1                              :        399907919
   j =  2                              :            46033
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 74                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.37
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 76                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 86                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 95                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.80
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 103                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.08
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 108                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
 p-value of test no 110                :    0.81
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
 p-value of test no 113                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.72
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.93
 p-value of test no 119                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.18
 p-value of test no 121                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.04
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.03
 p-value of test no 123                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 124                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.98
 p-value of test no 125                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 127                :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 128                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.79
 p-value of test no 129                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 131                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.49
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.12
 p-value of test no 134                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.96
 p-value of test no 137                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 140                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.46
 p-value of test no 141                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 144                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17565.93
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.87
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.11
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.40
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.74
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.01
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.32
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.15
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.27
 p-value of test no 153                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.19
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.63
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.21
 p-value of test no 156                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 157                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.28
 p-value of test no 158                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  196.09
 p-value of test no 159                :  5.7e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.54
 p-value of test no 160                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.15
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.29
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  447.09
 p-value of test no 163                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.28
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.41
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.35
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.94
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5029.77
 p-value of test no 168                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.20
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.64
 p-value of test no 170                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.66
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.20
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.26
 p-value of test no 173                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.11
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.09
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   21.31
 p-value of test no 176                :    0.05
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 177                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.04
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 179                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.89
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.67
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 185                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
 p-value of test no 191                :    0.67
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.33
 p-value of test no 196                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.79
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.05
 p-value of test no 203                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.60
 p-value of test no 207                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10213.06
 p-value of test no 211                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.57
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 214                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9912.06
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 221                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4839.27
 p-value of test no 222                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.16
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.08
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3862.46
 p-value of test no 228                :    0.9979
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11959.46
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12030.42
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.47
 p-value of test no 231                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999975050
 
 Normal statistic for number of bits   :   -0.20
 p-value of test no 232                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.12
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000089923
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.65
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 237                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 238                :    0.67
 
 Sample variance                       :    1.42
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 243                :    0.38
 
 Sample variance                       :    0.63
 p-value of test no 244                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    3.24
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.89
 p-value of test no 248                :    0.97
 
 Sample variance                       :    1.84
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.55
 p-value of test no 253                :    0.29
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:40.14
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs NP, t = 9            3.9e-4
  76  RandomWalk1 R (L=1000, r=0)     5.7e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35899
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 3                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 4                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 6                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 7                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 9                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 12                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5486
 p-value of test no 13                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4440
 p-value of test no 16                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 18                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 19                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.46
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    1.98
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     872
 p-value of test no 25                 :    0.82
 
 Stat. AD (mNP2)                       :    1.19
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.85
 p-value of test no 27                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.02
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.04
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.20
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 36                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 40                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.50
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    2.54
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 45                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.80
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.01
 p-value of test no 48                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.68
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.29
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.02
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.86
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.32
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  270.14
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  395.73
 p-value of test no 55                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1508.31
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7187.61
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 59                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 60                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   39.45
 p-value of test no 61                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 62                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.34
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.58
 p-value of test no 66                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.48
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5058.84
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 70                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908424
   j =  2                              :            45779
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45910
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869910
   j =  1                              :        399908183
   j =  2                              :            45904
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 72                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 74                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
 p-value of test no 79                 :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 92                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 104                :    0.81
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 105                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.88e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 110                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
 p-value of test no 113                :    0.42
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 116                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.78
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.75
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.19
 p-value of test no 120                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.58
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.65
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 124                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.99
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.24
 p-value of test no 129                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 130                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.95
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.90
 p-value of test no 134                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.51
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.94
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17283.98
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   55.50
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.92
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.55
 p-value of test no 148                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.68
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.64
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.36
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.13
 p-value of test no 153                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   47.01
 p-value of test no 154                :  3.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.90
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.64
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.93
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.58
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.07
 p-value of test no 159                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.77
 p-value of test no 160                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.70
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.98
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.07
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.03
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.07
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.67
 p-value of test no 166                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.09
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5183.55
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.41
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.59
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.49
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.59
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.48
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.48
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  260.29
 p-value of test no 175                :  2.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.65
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.20
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.93
 p-value of test no 178                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
 p-value of test no 186                :    0.9951
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 188                :    0.98
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
 p-value of test no 190                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.42
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.61
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.56
 p-value of test no 198                :    0.05
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 202                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.49
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 204                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.14
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.23
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.59
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 212                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 213                :    0.01
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10345.94
 p-value of test no 215                :  7.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 220                :    0.85
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.09
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 224                :    0.85
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.76
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.56
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4164.44
 p-value of test no 228                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11679.40
 p-value of test no 229                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11796.02
 p-value of test no 230                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.39
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000045133
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.55
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  7999799907
 
 Normal statistic for number of bits   :   -1.58
 p-value of test no 234                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 237                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 238                :    0.06
 
 Sample variance                       :    1.26
 p-value of test no 239                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 243                :    0.25
 
 Sample variance                       :    1.34
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.056
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.35
 p-value of test no 249                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.68
 p-value of test no 253                :    0.25
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:06.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35900
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 4                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 6                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 7                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 9                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5418
 p-value of test no 13                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4284
 p-value of test no 14                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 15                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4489
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 18                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7319
 p-value of test no 20                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7197
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 22                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 26                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.47
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.27
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     543
 p-value of test no 31                 :    0.9903
 
 Stat. AD (mNP2)                       :    3.69
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.32
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 34                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 35                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 38                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 39                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.53
 p-value of test no 40                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.08
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.19
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.75
 p-value of test no 47                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.74
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.96
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.93
 p-value of test no 50                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.37
 p-value of test no 51                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.88
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.01
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  456.41
 p-value of test no 55                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1401.19
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7023.33
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 59                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.89
 p-value of test no 61                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.23
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.28
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.79
 p-value of test no 67                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5012.43
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45960
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869960
   j =  1                              :        399908082
   j =  2                              :            45956
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45970
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869970
   j =  1                              :        399908060
   j =  2                              :            45970
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 78                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 81                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 87                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 88                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 90                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 95                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 97                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 105                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 107                :    0.13
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
 p-value of test no 110                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 111                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 112                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.22e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 114                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 115                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 118                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.14
 p-value of test no 119                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.49
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.82
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.76
 p-value of test no 122                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.69
 p-value of test no 123                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.31
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.38
 p-value of test no 129                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.16
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.65
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.59
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 137                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.40
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 144                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17337.03
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.33
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.43
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.33
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 150                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.21
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.00
 p-value of test no 152                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.64
 p-value of test no 153                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.46
 p-value of test no 155                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.80
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  194.84
 p-value of test no 157                :  4.3e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.52
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.56
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.61
 p-value of test no 160                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.92
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.02
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  433.75
 p-value of test no 163                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   97.41
 p-value of test no 164                :    0.9949
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.20
 p-value of test no 165                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.59
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.09
 p-value of test no 167                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5115.76
 p-value of test no 168                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.87
 p-value of test no 169                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  166.96
 p-value of test no 170                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.86
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.99
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.73
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.70
 p-value of test no 174                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.68
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.31
 p-value of test no 176                :    0.28
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.73
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.52
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.092
 p-value of test no 183                :    0.54
 
 Sample variance                       :    1.53
 p-value of test no 184                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.78e-3
 p-value of test no 190                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
 p-value of test no 191                :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-3
 p-value of test no 193                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 195                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.19
 p-value of test no 196                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.53
 p-value of test no 198                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.74
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.62
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 206                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.56
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.51
 p-value of test no 211                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 213                :    0.07
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10133.14
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 216                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.011
 p-value of test no 218                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.44
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4982.93
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 223                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5108.65
 p-value of test no 226                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4048.75
 p-value of test no 227                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.30
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12046.57
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11830.32
 p-value of test no 230                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.70
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999808061
 
 Normal statistic for number of bits   :   -1.52
 p-value of test no 232                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.41
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  7999967238
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
 p-value of test no 235                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 236                :    0.02
 
 Anderson-Darling statistic = A2       :    3.25
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.52
 p-value of test no 238                :  5.8e-3
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 243                :    0.22
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.54
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.086
 p-value of test no 253                :    0.53
 
 Sample variance                       :    1.32
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:52.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35901
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 5                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 6                  :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 8                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 11                 :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5428
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4392
 p-value of test no 14                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 15                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 16                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4356
 p-value of test no 17                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 19                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7405
 p-value of test no 20                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7296
 p-value of test no 21                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 23                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.16
 p-value of test no 26                 :    0.9976
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 30                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.95
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 33                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.21
 p-value of test no 35                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.23
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.56
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   19.43
 p-value of test no 47                 :  6.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.28
 p-value of test no 48                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.37
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.25
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.20
 p-value of test no 51                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.53
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.00
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  239.49
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  459.68
 p-value of test no 55                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1534.91
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7034.19
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 60                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.72
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 64                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.20
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.04
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   82.34
 p-value of test no 67                 :    0.9958
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.85
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907614
   j =  2                              :            46187
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46204
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870204
   j =  1                              :        399907597
   j =  2                              :            46194
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 72                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 76                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 77                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 79                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 86                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 99                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 102                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.42
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 107                :    0.95
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 109                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 111                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.13e-5
 p-value of test no 113                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 114                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 117                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  102.58
 p-value of test no 119                :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.84
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.27
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.90
 p-value of test no 122                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.19
 p-value of test no 123                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.38
 p-value of test no 124                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.00
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 128                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.92
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.61
 p-value of test no 133                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   12.01
 p-value of test no 135                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 136                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  109.40
 p-value of test no 141                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17366.98
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.17
 p-value of test no 146                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.92
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.15
 p-value of test no 148                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.51
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.69
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.42
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.34
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.88
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.37
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.63
 p-value of test no 155                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.10
 p-value of test no 156                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.85
 p-value of test no 157                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.05
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.47
 p-value of test no 159                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.95
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.12
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.17
 p-value of test no 163                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.30
 p-value of test no 164                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.88
 p-value of test no 165                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.96
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.69
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4780.39
 p-value of test no 168                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.43
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.79
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.41
 p-value of test no 171                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.59
 p-value of test no 172                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5059.80
 p-value of test no 173                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.53
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  223.04
 p-value of test no 175                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.14
 p-value of test no 176                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.58
 p-value of test no 177                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.41
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.60
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.64
 p-value of test no 183                :    0.05
 
 Sample variance                       :    0.89
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 186                :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 188                :    0.85
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 192                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.86
 p-value of test no 196                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 202                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.11
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.66
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.32
 p-value of test no 207                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.32
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 212                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.79
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9868.09
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 216                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 218                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 220                :    0.88
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4828.03
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 225                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4848.50
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4228.06
 p-value of test no 227                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.83
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12064.25
 p-value of test no 229                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11851.08
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.35
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999995408
 
 Normal statistic for number of bits   :  -0.036
 p-value of test no 232                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.74
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000099427
 
 Normal statistic for number of bits   :    0.79
 p-value of test no 234                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 237                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.62
 p-value of test no 239                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 243                :    0.37
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 246                :    0.92
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.44
 p-value of test no 248                :    0.93
 
 Sample variance                       :    0.55
 p-value of test no 249                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:28.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35902
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 9                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 10                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 11                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5380
 p-value of test no 13                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4215
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7478
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4417
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 17                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 22                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 23                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 24                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     883
 p-value of test no 25                 :    0.71
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 26                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.75
 p-value of test no 34                 :  4.0e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 35                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 36                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.85
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.41
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.25
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.27
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.82
 p-value of test no 49                 :  1.0e-2
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.09
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.56
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.82
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.72
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  177.43
 p-value of test no 54                 :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  479.68
 p-value of test no 55                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1431.36
 p-value of test no 56                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7074.22
 p-value of test no 57                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.80
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.67
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.08
 p-value of test no 66                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.62
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4946.78
 p-value of test no 68                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45990
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869990
   j =  1                              :        399908020
   j =  2                              :            45990
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45741
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869741
   j =  1                              :        399908526
   j =  2                              :            45725
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 78                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 80                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 93                 :  8.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    3.26
 p-value of test no 95                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
 p-value of test no 113                :    0.64
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 114                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 115                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 117                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 118                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.77
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.58
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.28
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.89
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.61
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.29
 p-value of test no 124                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.94
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.16
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 130                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 131                :    0.90
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 132                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.01
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.34
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 137                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.13
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17684.01
 p-value of test no 145                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.44
 p-value of test no 146                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.54
 p-value of test no 147                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.48
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.07
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   29.59
 p-value of test no 150                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.28
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.82
 p-value of test no 152                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.51
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.49
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.34
 p-value of test no 155                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.16
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.81
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.83
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.39
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.00
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.46
 p-value of test no 162                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.88
 p-value of test no 163                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.10
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.15
 p-value of test no 165                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.01
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.27
 p-value of test no 167                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4880.65
 p-value of test no 168                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.80
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.15
 p-value of test no 170                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.38
 p-value of test no 171                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.96
 p-value of test no 172                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5135.61
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.57
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.86
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.50
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.61
 p-value of test no 177                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.29
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.93
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 183                :    0.38
 
 Sample variance                       :    1.43
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
 p-value of test no 186                :    0.9901
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.35
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.99
 p-value of test no 189                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 192                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
 p-value of test no 194                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.85
 p-value of test no 196                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.92
 p-value of test no 198                :    0.77
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.45
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.28
 p-value of test no 207                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 210                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9782.49
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 214                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9815.14
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 217                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
 p-value of test no 220                :    0.9934
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4764.17
 p-value of test no 222                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4898.74
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.24
 p-value of test no 227                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4014.65
 p-value of test no 228                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11854.66
 p-value of test no 229                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.54
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.83
 p-value of test no 231                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999966908
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 232                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  7999930176
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 234                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 237                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 240                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.74
 p-value of test no 244                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 247                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.059
 p-value of test no 248                :    0.52
 
 Sample variance                       :    0.23
 p-value of test no 249                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35903
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1292
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334412
   j =  1                              :        599997416
   j =  2                              :             1292
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 7                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 9                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 12                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4249
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7107
 p-value of test no 15                 :    0.9933
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4214
 p-value of test no 16                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4367
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 18                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7192
 p-value of test no 20                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 21                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    0.22
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 27                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 29                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     615
 p-value of test no 31                 :    0.28
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 32                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 33                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.02
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 38                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:26.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.91
 p-value of test no 46                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.42
 p-value of test no 47                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.64
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.62
 p-value of test no 49                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.21
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.28
 p-value of test no 51                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.96
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.89
 p-value of test no 53                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.13
 p-value of test no 54                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  393.03
 p-value of test no 55                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1493.50
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.26
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.55
 p-value of test no 61                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 63                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.00
 p-value of test no 65                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.13
 p-value of test no 66                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.64
 p-value of test no 67                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5054.44
 p-value of test no 68                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46030
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870030
   j =  1                              :        399907942
   j =  2                              :            46026
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45914
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869914
   j =  1                              :        399908174
   j =  2                              :            45910
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 73                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 76                 :  5.9e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
 p-value of test no 77                 :    0.99
 
 Anderson-Darling statistic = A2       :    7.05
 p-value of test no 78                 :  3.3e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 81                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 84                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 85                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 86                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 95                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 99                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 102                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.40e-5
 p-value of test no 110                :    0.93
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 111                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 113                :    0.34
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      : -7.06e-4
 p-value of test no 115                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.08
 p-value of test no 119                :    0.9926
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.81
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.61
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.20
 p-value of test no 122                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.22
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.44
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.06
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    3.71
 p-value of test no 128                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.00
 p-value of test no 129                :  9.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.56
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.72
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.73
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.52
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.35
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17320.23
 p-value of test no 145                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.68
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.95
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 148                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.95
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.94
 p-value of test no 150                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.51
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.13
 p-value of test no 152                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.48
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.08
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.77
 p-value of test no 155                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.80
 p-value of test no 156                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.94
 p-value of test no 157                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.34
 p-value of test no 158                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.73
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.30
 p-value of test no 160                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.54
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.53
 p-value of test no 162                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.44
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.24
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.49
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.40
 p-value of test no 166                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.24
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5285.15
 p-value of test no 168                :  2.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.78
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.22
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.10
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.61
 p-value of test no 172                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5010.70
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.75
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.20
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.41
 p-value of test no 176                :    0.41
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.13
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    3.70
 p-value of test no 179                :  1.1e-4    *****
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 182                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 183                :    0.05
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 185                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 187                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 188                :    0.40
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 191                :    0.07
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 192                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
 p-value of test no 194                :    0.59
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 195                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.67
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.83
 p-value of test no 198                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 201                :    0.92
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 202                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.35
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.43
 p-value of test no 207                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 210                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9918.13
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10000.00
 p-value of test no 215                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 217                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 218                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 219                :  6.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    3.80
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4663.73
 p-value of test no 222                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 223                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.54
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.50
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.35
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4055.70
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11972.63
 p-value of test no 229                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11956.27
 p-value of test no 230                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.90
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000041419
 
 Normal statistic for number of bits   :    0.33
 p-value of test no 232                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.91
 p-value of test no 233                :    0.15
 
 
 -----------------------------------------------
 Total number of bits:  7999939479
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 238                :    0.27
 
 Sample variance                       :    2.02
 p-value of test no 239                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.14
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    0.90
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 246                :    0.99
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 247                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.12
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.07
 p-value of test no 249                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 252                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 253                :    0.26
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:42.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  46  MaxOft AD, t = 8                3.3e-4
  81  LinearComp, r = 29              1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35904
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 3                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 6                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 9                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5484
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4395
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7144
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 16                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7195
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 20                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7317
 p-value of test no 21                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 23                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 24                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     974
 p-value of test no 25                 :  7.7e-3
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 27                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 29                 :    0.87
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 30                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     577
 p-value of test no 31                 :    0.82
 
 Stat. AD (mNP2)                       :    1.21
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 40                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 41                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 42                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 45                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.71
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.66
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.82
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.90
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   31.35
 p-value of test no 51                 :    0.9942
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.44
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.10
 p-value of test no 53                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.86
 p-value of test no 54                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  427.23
 p-value of test no 55                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1444.77
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6974.75
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.57
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.51
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.70
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.07
 p-value of test no 67                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.79
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46292
 p-value of test no 70                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870292
   j =  1                              :        399907417
   j =  2                              :            46290
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45934
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869934
   j =  1                              :        399908135
   j =  2                              :            45928
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 74                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 76                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 77                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 81                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 85                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 87                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 88                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 90                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 94                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 97                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 102                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
 p-value of test no 110                :    0.28
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 111                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
 p-value of test no 112                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 113                :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 115                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 117                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 119                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.46
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.61
 p-value of test no 121                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.52
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.21
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.87
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.32
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.60
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.74
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.29
 p-value of test no 133                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.08
 p-value of test no 134                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.94
 p-value of test no 135                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 137                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 138                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 139                :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 140                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  137.57
 p-value of test no 141                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17540.86
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.66
 p-value of test no 146                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.22
 p-value of test no 147                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.54
 p-value of test no 148                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.29
 p-value of test no 149                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.58
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.44
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.39
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.38
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.54
 p-value of test no 154                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.22
 p-value of test no 155                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.26
 p-value of test no 156                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.66
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.24
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.89
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.27
 p-value of test no 160                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.42
 p-value of test no 161                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.83
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  532.39
 p-value of test no 163                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.32
 p-value of test no 164                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  103.12
 p-value of test no 165                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.98
 p-value of test no 166                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.48
 p-value of test no 167                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.89
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.09
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.52
 p-value of test no 170                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.25
 p-value of test no 171                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.15
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4907.01
 p-value of test no 173                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.09
 p-value of test no 174                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.46
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.74
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.71
 p-value of test no 177                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.84
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.37
 p-value of test no 179                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 183                :    0.46
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.69
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 188                :    0.68
 
 Sample variance                       :    1.04
 p-value of test no 189                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
 p-value of test no 194                :    0.96
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 195                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.92
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.98
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 201                :    0.13
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.28
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 205                :    0.79
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.06
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9966.54
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 213                :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 214                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9800.35
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 216                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 217                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4986.00
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 225                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4907.08
 p-value of test no 226                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.58
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3994.73
 p-value of test no 228                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11775.66
 p-value of test no 229                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.24
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.97
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000038938
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.10
 p-value of test no 233                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000169783
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.62
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 238                :    0.56
 
 Sample variance                       :    0.74
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 240                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 241                :    0.05
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.11
 p-value of test no 243                :    0.02
 
 Sample variance                       :    1.08
 p-value of test no 244                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 247                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 248                :    0.35
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 252                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.21
 p-value of test no 253                :    0.89
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:27.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35905
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 8                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 18                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 19                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7151
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 27                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 28                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.87
 p-value of test no 29                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 30                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     581
 p-value of test no 31                 :    0.77
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 36                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.59
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 44                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 45                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.85
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.69
 p-value of test no 47                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.76
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   34.44
 p-value of test no 49                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 50                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.22
 p-value of test no 51                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.21
 p-value of test no 52                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.59
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.10
 p-value of test no 54                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.47
 p-value of test no 55                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.02
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7184.65
 p-value of test no 57                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 60                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.69
 p-value of test no 61                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 62                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 63                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   68.52
 p-value of test no 65                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.73
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.02
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4988.02
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908234
   j =  2                              :            45880
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 71                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908231
   j =  2                              :            45880
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 72                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 78                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 83                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 85                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 87                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 88                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 97                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 98                 :    0.97
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 99                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 101                :    0.93
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 103                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 105                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 106                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.77e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.79
 p-value of test no 115                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 116                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 117                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.50
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.11
 p-value of test no 120                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.92
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 122                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.29
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.84
 p-value of test no 124                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.12
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 126                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.91
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 132                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   58.79
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.04
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.47
 p-value of test no 135                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.40
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.07
 p-value of test no 141                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17463.92
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.35
 p-value of test no 146                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.08
 p-value of test no 147                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.46
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.18
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.23
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.87
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.51
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.18
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.87
 p-value of test no 154                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.93
 p-value of test no 155                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.87
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.38
 p-value of test no 157                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.88
 p-value of test no 158                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.14
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.57
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.58
 p-value of test no 162                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.29
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  108.49
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.72
 p-value of test no 165                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.55
 p-value of test no 166                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.43
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5063.59
 p-value of test no 168                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  410.40
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.52
 p-value of test no 170                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.95
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.61
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.64
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.12
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.53
 p-value of test no 175                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.24
 p-value of test no 176                :    0.60
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.90
 p-value of test no 177                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.91
 p-value of test no 178                :    0.62
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 182                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.092
 p-value of test no 183                :    0.46
 
 Sample variance                       :    1.57
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 185                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 188                :    0.15
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.28
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 192                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
 p-value of test no 193                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.94
 p-value of test no 196                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.81
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 202                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.03
 p-value of test no 203                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 204                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.87
 p-value of test no 207                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.67
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 212                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10227.40
 p-value of test no 215                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 216                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.47
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 221                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4880.59
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.27
 p-value of test no 226                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4128.46
 p-value of test no 227                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4036.62
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12016.12
 p-value of test no 229                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11655.79
 p-value of test no 230                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.59
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000162991
 
 Normal statistic for number of bits   :    1.29
 p-value of test no 232                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   92.83
 p-value of test no 233                :  8.0e-4    *****
 
 
 -----------------------------------------------
 Total number of bits:  7999917981
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 234                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.36
 p-value of test no 239                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
 p-value of test no 241                : 1 -  7.7e-5    *****
 
 Anderson-Darling statistic = A2       :    3.43
 p-value of test no 242                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.87
 p-value of test no 243                :    0.9980
 
 Sample variance                       :    2.00
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 245                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.18
 p-value of test no 249                :    0.9963
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  102  Run of bits, r = 27             8.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35906
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 5                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 6                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 8                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 10                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 12                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5430
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4294
 p-value of test no 14                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 15                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4368
 p-value of test no 17                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7426
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 19                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.67
 p-value of test no 22                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.53
 p-value of test no 24                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     848
 p-value of test no 25                 :    0.96
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 26                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.69
 p-value of test no 28                 :    0.14
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 32                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.16
 p-value of test no 33                 :    0.9975
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.80
 p-value of test no 35                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     286
 p-value of test no 37                 :    0.78
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 38                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.87
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 41                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 44                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.30
 p-value of test no 45                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.24
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.45
 p-value of test no 47                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.79
 p-value of test no 48                 :  7.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.29
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.54
 p-value of test no 50                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.55
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.80
 p-value of test no 52                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.03
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.27
 p-value of test no 54                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.84
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1502.54
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6886.88
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 60                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.53
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 63                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.42
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.61
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.05
 p-value of test no 67                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4992.79
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45861
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869861
   j =  1                              :        399908279
   j =  2                              :            45859
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45575
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869575
   j =  1                              :        399908851
   j =  2                              :            45573
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 73                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.22
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 85                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 87                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 88                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 92                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.11
 p-value of test no 95                 : 1 -  7.4e-5    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.17
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 102                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 103                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 105                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 106                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
 p-value of test no 110                :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 111                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
 p-value of test no 112                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
 p-value of test no 113                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 114                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 115                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -3.03
 p-value of test no 116                :    0.9988
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.00
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 118                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.02
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.45
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.38
 p-value of test no 121                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.25
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.04
 p-value of test no 123                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.77
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.47
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 127                :    0.88
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.17
 p-value of test no 129                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 131                :    0.14
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 132                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.96
 p-value of test no 133                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.34
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 140                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.02
 p-value of test no 141                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 144                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17566.17
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.43
 p-value of test no 146                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.33
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.49
 p-value of test no 148                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.86
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.20
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.25
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.96
 p-value of test no 152                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.03
 p-value of test no 153                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.89
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.78
 p-value of test no 155                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.60
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.65
 p-value of test no 157                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.96
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.96
 p-value of test no 159                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.79
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.42
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.38
 p-value of test no 162                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.79
 p-value of test no 163                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.24
 p-value of test no 164                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.48
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.74
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.81
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.75
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.51
 p-value of test no 169                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.64
 p-value of test no 170                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.46
 p-value of test no 171                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.26
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5088.69
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.16
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.06
 p-value of test no 175                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.77
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 177                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.40
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.25
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.35
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 182                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 183                :    0.61
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 185                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 186                :    0.05
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 188                :    0.11
 
 Sample variance                       :    1.51
 p-value of test no 189                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    1.74
 p-value of test no 196                :    0.99
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.74
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.94
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 206                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.94
 p-value of test no 207                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.65
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9997.94
 p-value of test no 211                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.33
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 217                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 218                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.92
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.35
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.70
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4054.76
 p-value of test no 228                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11747.57
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11920.76
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   80.99
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  7999995183
 
 Normal statistic for number of bits   :  -0.038
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.17
 p-value of test no 233                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000077209
 
 Normal statistic for number of bits   :    0.61
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.30
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 237                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 238                :    0.32
 
 Sample variance                       :    0.63
 p-value of test no 239                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.74
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.69
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 246                :    0.06
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 248                :    0.45
 
 Sample variance                       :    0.21
 p-value of test no 249                :    0.9936
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 250                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.25
 p-value of test no 254                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:05.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35907
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 6                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 7                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 9                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 11                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 12                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5431
 p-value of test no 13                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 15                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 18                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 19                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 21                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.27
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     600
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.27
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 33                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.07
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    3.77
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     330
 p-value of test no 37                 :    0.05
 
 Stat. AD (mNP2)                       :    3.62
 p-value of test no 38                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.89
 p-value of test no 40                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 41                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.81
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.61
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.86
 p-value of test no 48                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.89
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.64
 p-value of test no 50                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.18
 p-value of test no 51                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.85
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.95
 p-value of test no 53                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.06
 p-value of test no 54                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  426.80
 p-value of test no 55                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1511.00
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7002.89
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 60                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.60
 p-value of test no 61                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 62                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.02
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.81
 p-value of test no 67                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5037.92
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46221
 p-value of test no 70                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870221
   j =  1                              :        399907564
   j =  2                              :            46209
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45922
 p-value of test no 71                 :    0.42
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869922
   j =  1                              :        399908157
   j =  2                              :            45920
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 85                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 88                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 92                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 95                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 99                 :    0.9963
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 100                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 101                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 104                :    0.93
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 111                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 114                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 116                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 117                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.05
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.33
 p-value of test no 120                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.24
 p-value of test no 121                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.97
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.06
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.68
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.67
 p-value of test no 125                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 127                :    0.97
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 128                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.36
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.70
 p-value of test no 133                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.60
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.65
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 136                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 139                :    0.59
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 140                :    0.9913
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.21
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 143                :    0.80
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.40
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.65
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.64
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.59
 p-value of test no 148                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.45
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.20
 p-value of test no 150                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   61.03
 p-value of test no 151                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.34
 p-value of test no 152                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.33
 p-value of test no 153                :  5.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.25
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.54
 p-value of test no 156                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.62
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.56
 p-value of test no 158                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.59
 p-value of test no 159                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.61
 p-value of test no 160                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.96
 p-value of test no 161                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.69
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.70
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.29
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.08
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.96
 p-value of test no 166                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.59
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5200.69
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.75
 p-value of test no 169                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.04
 p-value of test no 170                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.70
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.88
 p-value of test no 172                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.91
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.72
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.88
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 177                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.12
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.55
 p-value of test no 179                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 181                :    0.22
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    1.71
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 195                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.73
 p-value of test no 196                :    0.37
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.55
 p-value of test no 198                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 200                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 202                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  236.96
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 204                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    4.61
 p-value of test no 206                :  4.6e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  145.63
 p-value of test no 207                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 208                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9798.64
 p-value of test no 211                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 214                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.11
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.53
 p-value of test no 216                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.74
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.72
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 224                :    0.78
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.28
 p-value of test no 226                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4033.64
 p-value of test no 227                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4137.04
 p-value of test no 228                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11689.91
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11354.69
 p-value of test no 230                :    0.9990    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.22
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000071776
 
 Normal statistic for number of bits   :    0.57
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.66
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000175129
 
 Normal statistic for number of bits   :    1.38
 p-value of test no 234                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 237                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.41
 p-value of test no 238                :    0.92
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    2.10
 p-value of test no 244                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 246                :    0.9902
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.98
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 1.93e-3
 p-value of test no 251                :    0.9980
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 253                :    0.95
 
 Sample variance                       :    1.44
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:58.12
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  100  HammingIndep, L=1200, r=25      0.9990 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35908
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 4                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 5                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 8                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 10                 :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 12                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 14                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7447
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4311
 p-value of test no 17                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 20                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 22                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     886
 p-value of test no 25                 :    0.67
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 26                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.79
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    3.12
 p-value of test no 30                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     541
 p-value of test no 31                 :    0.9923
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 32                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     273
 p-value of test no 37                 :    0.94
 
 Stat. AD (mNP2)                       :    1.26
 p-value of test no 38                 :    0.25
 
 Stat. AD after spacings (mNP2-S)      :    0.77
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.00
 p-value of test no 41                 :    0.35
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    2.01
 p-value of test no 45                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.92
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.91
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.42
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.78
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.33
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.32
 p-value of test no 51                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.54
 p-value of test no 52                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.70
 p-value of test no 53                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.38
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  493.23
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1360.44
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7197.02
 p-value of test no 57                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   36.70
 p-value of test no 61                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.30
 p-value of test no 65                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.97
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.85
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4956.74
 p-value of test no 68                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46265
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870265
   j =  1                              :        399907471
   j =  2                              :            46263
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45789
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869789
   j =  1                              :        399908424
   j =  2                              :            45785
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 80                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 85                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 98                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 101                :    0.68
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 105                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 109                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
 p-value of test no 112                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
 p-value of test no 113                :    0.59
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.079
 p-value of test no 115                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.58
 p-value of test no 116                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 117                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.04
 p-value of test no 119                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.89
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.88
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.23
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.69
 p-value of test no 123                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.94
 p-value of test no 124                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.86
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 126                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.12
 p-value of test no 129                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.45
 p-value of test no 133                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.33
 p-value of test no 134                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.57
 p-value of test no 135                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 140                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.39
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 144                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17587.98
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   18.92
 p-value of test no 146                :    0.9914
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.34
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.93
 p-value of test no 148                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.44
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.36
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.36
 p-value of test no 151                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.55
 p-value of test no 152                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.23
 p-value of test no 153                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.86
 p-value of test no 154                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.11
 p-value of test no 155                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.16
 p-value of test no 156                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.06
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.35
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.53
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.75
 p-value of test no 160                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.31
 p-value of test no 161                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.56
 p-value of test no 162                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.23
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.71
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.00
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.77
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.19
 p-value of test no 167                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.67
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.34
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  238.30
 p-value of test no 170                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.38
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.49
 p-value of test no 172                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.94
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.15
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.87
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.75
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.91
 p-value of test no 178                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.40
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 181                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 182                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 183                :    0.52
 
 Sample variance                       :    0.95
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.72
 p-value of test no 189                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.32
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 195                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.37
 p-value of test no 196                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.31
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.61
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.94
 p-value of test no 203                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 206                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  227.52
 p-value of test no 207                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 210                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9934.15
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.83
 p-value of test no 215                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 220                :    0.96
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 221                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4739.99
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.30
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4060.66
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4141.76
 p-value of test no 228                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.70
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12002.77
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.19
 p-value of test no 231                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  8000068119
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.92
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000058210
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 234                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.22
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 237                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 238                :    0.25
 
 Sample variance                       :    0.43
 p-value of test no 239                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 241                :    0.03
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.89
 p-value of test no 243                :    0.03
 
 Sample variance                       :    0.75
 p-value of test no 244                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 248                :    0.27
 
 Sample variance                       :    1.25
 p-value of test no 249                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35909
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 3                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 9                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5316
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 15                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7216
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     885
 p-value of test no 25                 :    0.68
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 26                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    4.22
 p-value of test no 27                 :  6.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 28                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 29                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    1.48
 p-value of test no 30                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 36                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.67
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 39                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.58
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.21
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.84
 p-value of test no 48                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.49
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.76
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.31
 p-value of test no 51                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 52                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.69
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  234.52
 p-value of test no 54                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.11
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1435.58
 p-value of test no 56                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6945.87
 p-value of test no 57                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 60                 :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.85
 p-value of test no 61                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.57
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.73
 p-value of test no 66                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.00
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4978.43
 p-value of test no 68                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46013
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870013
   j =  1                              :        399907978
   j =  2                              :            46005
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46483
 p-value of test no 71                 :  2.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870483
   j =  1                              :        399907037
   j =  2                              :            46477
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 74                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.36
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 78                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 84                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 85                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 88                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 91                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 92                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.52
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 106                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 108                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 4.02e-4
 p-value of test no 110                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.90
 p-value of test no 111                :  3.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
 p-value of test no 113                :    0.33
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 115                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.46
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 117                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.63
 p-value of test no 119                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.72
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.83
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.91
 p-value of test no 122                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.92
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.97
 p-value of test no 124                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.35
 p-value of test no 125                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
 p-value of test no 127                :    0.9943
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 128                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.13
 p-value of test no 129                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 130                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 131                :    0.91
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.01
 p-value of test no 133                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 134                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 135                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.77
 p-value of test no 137                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.53
 p-value of test no 141                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 143                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17413.45
 p-value of test no 145                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   19.11
 p-value of test no 146                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.11
 p-value of test no 147                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.34
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.93
 p-value of test no 149                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.83
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.40
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.08
 p-value of test no 152                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.49
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.30
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.45
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.43
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.16
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.80
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.55
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.20
 p-value of test no 160                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.00
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.80
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.21
 p-value of test no 163                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.11
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.90
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.50
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.58
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4834.97
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.86
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  196.10
 p-value of test no 170                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.83
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.28
 p-value of test no 172                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.67
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.52
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.92
 p-value of test no 175                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.73
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.40
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.03
 p-value of test no 178                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.38
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 180                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 186                :    0.89
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.20
 p-value of test no 188                :    0.89
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 192                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.54
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.87
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.28
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 206                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.56
 p-value of test no 207                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 208                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 210                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9808.83
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 214                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.47
 p-value of test no 215                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.065
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 218                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 219                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 221                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.32
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.40
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4938.50
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4044.22
 p-value of test no 227                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.03
 p-value of test no 228                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11884.85
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11753.65
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.64
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  8000005536
 
 Normal statistic for number of bits   :   0.044
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.79
 p-value of test no 233                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000145594
 
 Normal statistic for number of bits   :    1.15
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.08
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.52
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 242                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.77
 p-value of test no 243                :    0.78
 
 Sample variance                       :    0.24
 p-value of test no 244                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 247                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 248                :    0.90
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 250                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 253                :    0.10
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:02.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35910
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 4                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 5                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1301
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334421
   j =  1                              :        599997398
   j =  2                              :             1301
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1274
 p-value of test no 8                  :    0.9929
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334394
   j =  1                              :        599997452
   j =  2                              :             1274
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 9                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 10                 :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 11                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 12                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4485
 p-value of test no 14                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 17                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 20                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.00
 p-value of test no 24                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 27                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     608
 p-value of test no 31                 :    0.38
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 34                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.14
 p-value of test no 35                 :  7.8e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    0.15
 p-value of test no 36                 :    0.9982
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.04
 p-value of test no 41                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 44                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.06
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.70
 p-value of test no 47                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.23
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.22
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.64
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   30.94
 p-value of test no 51                 :    0.9951
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.60
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.98
 p-value of test no 53                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.92
 p-value of test no 54                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.86
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1383.39
 p-value of test no 56                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7140.05
 p-value of test no 57                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   16.46
 p-value of test no 61                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 62                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 64                 :    0.9956
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.98
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.19
 p-value of test no 66                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  155.67
 p-value of test no 67                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.24
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45525
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869525
   j =  1                              :        399908952
   j =  2                              :            45521
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45750
 p-value of test no 71                 :    0.73
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869750
   j =  1                              :        399908504
   j =  2                              :            45742
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 80                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 81                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 84                 :    0.9998    *****
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 85                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 92                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 93                 :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 94                 :    0.9916
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 99                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 104                :    0.64
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 107                :    0.63
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 108                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
 p-value of test no 110                :    0.68
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 114                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 115                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.70
 p-value of test no 116                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.088
 p-value of test no 117                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 118                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.33
 p-value of test no 119                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.80
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.01
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.75
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.95
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.67
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.19
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 126                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 128                :    0.9941
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.74
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.19
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.17
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.12
 p-value of test no 136                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.17
 p-value of test no 137                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 139                :    0.17
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.98
 p-value of test no 141                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.43
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17380.59
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.24
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.27
 p-value of test no 147                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.06
 p-value of test no 148                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.31
 p-value of test no 149                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.64
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.58
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.35
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.46
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.66
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.69
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  116.04
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.97
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.48
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.04
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.00
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.33
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.13
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.20
 p-value of test no 163                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.70
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.23
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.72
 p-value of test no 166                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.88
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.79
 p-value of test no 168                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.16
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.12
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.62
 p-value of test no 171                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.75
 p-value of test no 172                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.98
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.01
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  165.60
 p-value of test no 175                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.74
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -1.49e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.26
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.28
 p-value of test no 179                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 188                :    0.75
 
 Sample variance                       :    1.31
 p-value of test no 189                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
 p-value of test no 191                :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 192                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
 p-value of test no 193                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 195                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.88
 p-value of test no 196                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.10
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.97
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 204                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  186.57
 p-value of test no 207                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.09e-3
 p-value of test no 208                :    0.9968
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.26
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 210                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10266.20
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 212                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    2.21
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9811.48
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.94
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 220                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4826.94
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.22
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.59
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4096.32
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11546.71
 p-value of test no 229                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11915.79
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.33
 p-value of test no 231                :    0.90
 
 
 -----------------------------------------------
 Total number of bits:  8000010390
 
 Normal statistic for number of bits   :   0.082
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.89
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999823274
 
 Normal statistic for number of bits   :   -1.40
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.09
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 237                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.03
 p-value of test no 238                :    0.02
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 241                :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 242                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 243                :    0.35
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 248                :    0.43
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.15
 p-value of test no 253                :    0.87
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.80
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:12.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35911
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 3                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 4                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 5                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1492
 p-value of test no 11                 :  3.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334612
   j =  1                              :        599997016
   j =  2                              :             1492
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5343
 p-value of test no 13                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4328
 p-value of test no 16                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 17                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 18                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7384
 p-value of test no 19                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 20                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.23
 p-value of test no 23                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    3.36
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     843
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.94
 p-value of test no 26                 :    0.39
 
 Stat. AD after spacings (mNP2-S)      :    0.57
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     619
 p-value of test no 31                 :    0.22
 
 Stat. AD (mNP2)                       :    1.23
 p-value of test no 32                 :    0.26
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 33                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 34                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.38
 p-value of test no 35                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 36                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.03
 p-value of test no 41                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 42                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 45                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.84
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.37
 p-value of test no 47                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.38
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.24
 p-value of test no 49                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.71
 p-value of test no 51                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.78
 p-value of test no 52                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.17
 p-value of test no 53                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.41
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.50
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.10
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7309.44
 p-value of test no 57                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 58                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.60
 
 Anderson-Darling statistic = A2       :    2.23
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.39
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 64                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.75
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.83
 p-value of test no 66                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.12
 p-value of test no 67                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.11
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908125
   j =  2                              :            45930
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908897
   j =  2                              :            45544
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 73                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 74                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 76                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 79                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  8.3e-3
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 81                 :  5.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
 p-value of test no 86                 :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 87                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
 p-value of test no 94                 :    0.9933
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 101                :    0.28
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 105                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 107                :    0.97
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 108                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
 p-value of test no 110                :    0.04
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 111                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
 p-value of test no 112                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.31
 p-value of test no 115                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.48
 p-value of test no 116                :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 118                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.70
 p-value of test no 119                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.70
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.08
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.02
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.32
 p-value of test no 123                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.17
 p-value of test no 124                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.63
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.02
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.38
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.43
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.42
 p-value of test no 136                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.37
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 142                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.20
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 144                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.12
 p-value of test no 145                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.10
 p-value of test no 146                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.44
 p-value of test no 147                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.44
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.57
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.27
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.51
 p-value of test no 151                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   61.26
 p-value of test no 152                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.66
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 154                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.76
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.88
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.81
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  549.51
 p-value of test no 158                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.46
 p-value of test no 159                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.36
 p-value of test no 160                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.22
 p-value of test no 161                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.25
 p-value of test no 162                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.03
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.53
 p-value of test no 164                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.52
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.53
 p-value of test no 166                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.81
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5176.01
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.19
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.84
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.60
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.02
 p-value of test no 172                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5100.83
 p-value of test no 173                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.46
 p-value of test no 174                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.99
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 177                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.23
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.95
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.60
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.31
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 187                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 188                :    0.24
 
 Sample variance                       :    1.96
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
 p-value of test no 190                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 192                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
 p-value of test no 193                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.36
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.55
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.19
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.48
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 206                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.08
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.65
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 212                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 214                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10158.26
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.052
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.87
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 219                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.66
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 223                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.08
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4995.41
 p-value of test no 226                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.48
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4114.04
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11924.52
 p-value of test no 229                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11942.15
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000002638
 
 Normal statistic for number of bits   :   0.021
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.54
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  8000074038
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 234                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 235                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 237                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 238                :    0.87
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 241                :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 242                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.47
 p-value of test no 243                :    0.68
 
 Sample variance                       :    0.88
 p-value of test no 244                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 245                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.58
 p-value of test no 246                :  4.4e-4    *****
 
 Anderson-Darling statistic = A2       :    5.66
 p-value of test no 247                :  1.5e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.89
 p-value of test no 248                :  1.9e-3
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    0.51
 p-value of test no 254                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:48.62
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           3.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35912
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 5                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 6                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1450
 p-value of test no 9                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334570
   j =  1                              :        599997100
   j =  2                              :             1450
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 12                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4411
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 15                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 17                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 20                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 21                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 22                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.84
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.45
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 29                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     602
 p-value of test no 31                 :    0.47
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.85
 p-value of test no 34                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 35                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    1.00
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.19
 p-value of test no 39                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 40                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    4.32
 p-value of test no 44                 :  6.1e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 45                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.80
 p-value of test no 46                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.86
 p-value of test no 47                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.76
 p-value of test no 48                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.85
 p-value of test no 49                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.52
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.35
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.41
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.02
 p-value of test no 53                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  274.55
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.50
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1460.89
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6809.08
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 60                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   50.74
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 64                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.76
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.70
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.22
 p-value of test no 67                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.67
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908208
   j =  2                              :            45896
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46315
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870315
   j =  1                              :        399907374
   j =  2                              :            46307
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 73                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 78                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 80                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 81                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 84                 :    0.96
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.18
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 99                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 100                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 103                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 105                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 107                :    0.04
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 108                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.038
 p-value of test no 115                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 116                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.11
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 118                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   94.71
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.86
 p-value of test no 120                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.17
 p-value of test no 121                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.85
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.38
 p-value of test no 123                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.61
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.74
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 126                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 128                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.32
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   55.91
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.80
 p-value of test no 134                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 139                :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  153.17
 p-value of test no 141                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.44
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 144                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17367.83
 p-value of test no 145                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.23
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.00
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.91
 p-value of test no 148                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.18
 p-value of test no 149                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.41
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.27
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.75
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.95
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.75
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.97
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.62
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.70
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.97
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.63
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.73
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.34
 p-value of test no 162                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  533.78
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.07
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.73
 p-value of test no 165                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.53
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.33
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4866.03
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.99
 p-value of test no 169                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.24
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.82
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.96
 p-value of test no 172                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5049.87
 p-value of test no 173                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.03
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.44
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.00
 p-value of test no 176                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 177                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.27
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.066
 p-value of test no 179                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.082
 p-value of test no 183                :    0.53
 
 Sample variance                       :    1.31
 p-value of test no 184                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.32
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.060
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.28
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 192                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 193                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-3
 p-value of test no 194                :    0.98
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 195                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.26
 p-value of test no 196                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.68
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.70
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 206                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.69
 p-value of test no 207                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10053.90
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 212                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.71
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9886.15
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.078
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 219                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.75
 p-value of test no 222                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.58
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4841.15
 p-value of test no 226                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4158.19
 p-value of test no 227                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.26
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11817.42
 p-value of test no 229                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11861.70
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.90
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999985241
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 232                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.74
 p-value of test no 233                :    0.41
 
 
 -----------------------------------------------
 Total number of bits:  7999901610
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 237                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 243                :    0.29
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 247                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 248                :    0.32
 
 Sample variance                       :    2.03
 p-value of test no 249                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 252                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 253                :    0.58
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:08.40
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35913
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 5                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 6                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 7                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5404
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4198
 p-value of test no 16                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 17                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 19                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7352
 p-value of test no 20                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    3.52
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     830
 p-value of test no 25                 :    0.9904
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 29                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 34                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 35                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    1.74
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.30
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 42                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     130
 p-value of test no 43                 :    0.95
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 44                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.39
 p-value of test no 46                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.08
 p-value of test no 48                 :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.79
 p-value of test no 49                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.94
 p-value of test no 50                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.13
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.47
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.05
 p-value of test no 53                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  258.67
 p-value of test no 54                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  468.86
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.82
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6930.70
 p-value of test no 57                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 59                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.46
 p-value of test no 61                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 63                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.32
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:27.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.37
 p-value of test no 66                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.85
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5071.01
 p-value of test no 68                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46177
 p-value of test no 70                 :    0.08
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870177
   j =  1                              :        399907650
   j =  2                              :            46169
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46015
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870015
   j =  1                              :        399907971
   j =  2                              :            46013
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 72                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 73                 :    0.85
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 77                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 78                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 80                 :    0.86
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 81                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 86                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 90                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 92                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 93                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 95                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 100                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 101                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.32
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 106                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 108                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 116                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 117                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.32
 p-value of test no 119                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.56
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.93
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.91
 p-value of test no 123                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.14
 p-value of test no 124                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.13
 p-value of test no 125                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 126                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 127                :    0.94
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 128                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.53
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 132                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.70
 p-value of test no 133                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.19
 p-value of test no 134                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.07
 p-value of test no 135                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.80
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.85
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.27
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 144                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17410.09
 p-value of test no 145                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.12
 p-value of test no 146                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.23
 p-value of test no 147                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.38
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.50
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.99
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.77
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   55.48
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.64
 p-value of test no 153                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.77
 p-value of test no 154                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.78
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.25
 p-value of test no 156                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.42
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  535.62
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.44
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.36
 p-value of test no 160                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.26
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.49
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.81
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.41
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.14
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.88
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.31
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5185.17
 p-value of test no 168                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.94
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.12
 p-value of test no 170                :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.21
 p-value of test no 171                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.40
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.94
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.16
 p-value of test no 174                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.98
 p-value of test no 175                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.81
 p-value of test no 176                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.00
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.22
 p-value of test no 178                :    0.08
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.77
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 180                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 182                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.01
 p-value of test no 183                :    0.16
 
 Sample variance                       :    1.02
 p-value of test no 184                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 188                :    0.35
 
 Sample variance                       :    1.30
 p-value of test no 189                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 192                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
 p-value of test no 193                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
 p-value of test no 194                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.09
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.62
 p-value of test no 198                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.25
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.52
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 206                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.12
 p-value of test no 207                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.43
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.04
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 212                :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 213                :    0.98
 
 Anderson-Darling statistic = A2       :    3.75
 p-value of test no 214                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9640.10
 p-value of test no 215                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.20
 p-value of test no 216                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 217                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.13
 p-value of test no 218                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.37
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.11
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 224                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.13
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.45
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4127.63
 p-value of test no 228                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12114.33
 p-value of test no 229                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11680.36
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.16
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  8000098344
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.11
 p-value of test no 233                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000169486
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 234                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 238                :    0.43
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    4.45
 p-value of test no 242                :  5.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.71
 p-value of test no 243                :  3.3e-3
 
 Sample variance                       :    0.67
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 245                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 246                :  3.5e-3
 
 Anderson-Darling statistic = A2       :    3.12
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 248                :    0.04
 
 Sample variance                       :    1.34
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.71
 p-value of test no 253                :    0.24
 
 Sample variance                       :    1.42
 p-value of test no 254                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:38.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35914
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 5                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 7                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 11                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5426
 p-value of test no 13                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 15                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4299
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 18                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 19                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7520
 p-value of test no 20                 :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.81
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    8.14
 p-value of test no 23                 :  1.0e-4    *****
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 26                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 28                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 29                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.01
 p-value of test no 30                 :    0.35
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     610
 p-value of test no 31                 :    0.35
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 33                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 34                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.44
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 36                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     318
 p-value of test no 37                 :    0.16
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.19
 p-value of test no 41                 :    0.9930
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 44                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.40
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.29
 p-value of test no 48                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.35
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.63
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.43
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.72
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.14
 p-value of test no 53                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.19
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  385.09
 p-value of test no 55                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1458.94
 p-value of test no 56                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6920.45
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.30
 p-value of test no 61                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   86.43
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.86
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.56
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4907.53
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45941
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869941
   j =  1                              :        399908120
   j =  2                              :            45937
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45791
 p-value of test no 71                 :    0.66
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869791
   j =  1                              :        399908423
   j =  2                              :            45781
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.72
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  3.5e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 78                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 91                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 97                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 99                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 102                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 105                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 107                :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 108                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 114                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.39
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 116                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 117                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 118                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.21
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.79
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.69
 p-value of test no 121                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.18
 p-value of test no 122                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.10
 p-value of test no 123                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.87
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.93
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.55
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.94
 p-value of test no 129                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 130                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.74
 p-value of test no 133                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.49
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.71
 p-value of test no 135                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.82
 p-value of test no 136                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 139                :    0.95
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  103.72
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 143                :    0.93
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 144                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17240.94
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.70
 p-value of test no 146                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.52
 p-value of test no 147                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.19
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.31
 p-value of test no 149                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.44
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.83
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   59.70
 p-value of test no 152                :  5.7e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.41
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.48
 p-value of test no 154                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.06
 p-value of test no 155                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.27
 p-value of test no 156                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.58
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  514.87
 p-value of test no 158                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.33
 p-value of test no 159                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.22
 p-value of test no 160                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.53
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.92
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.66
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.12
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.08
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.23
 p-value of test no 166                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.92
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4910.25
 p-value of test no 168                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.67
 p-value of test no 169                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.95
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.18
 p-value of test no 171                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  335.30
 p-value of test no 172                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.30
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.46
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.86
 p-value of test no 175                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.61
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.93
 p-value of test no 177                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.18
 p-value of test no 178                :    0.77
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.41
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 181                :    0.09
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 182                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.40
 p-value of test no 183                :    0.08
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 185                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 186                :  2.5e-4    *****
 
 Anderson-Darling statistic = A2       :    6.46
 p-value of test no 187                :  6.4e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.06
 p-value of test no 188                :  1.1e-3
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
 p-value of test no 190                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 193                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 195                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.48
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.35
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.53
 p-value of test no 203                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 205                :    0.84
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 206                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.57
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 208                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.45
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.64
 p-value of test no 211                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9896.71
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 217                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.16
 p-value of test no 218                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 219                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4985.53
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.06
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4020.31
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.27
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11931.79
 p-value of test no 229                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11688.11
 p-value of test no 230                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.10
 p-value of test no 231                :    0.26
 
 
 -----------------------------------------------
 Total number of bits:  7999992879
 
 Normal statistic for number of bits   :  -0.056
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.78
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000034651
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 234                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.029
 p-value of test no 238                :    0.51
 
 Sample variance                       :    1.00
 p-value of test no 239                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 240                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.79
 p-value of test no 243                :    0.04
 
 Sample variance                       :    0.66
 p-value of test no 244                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    2.57
 p-value of test no 249                :  5.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 251                :    0.97
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 252                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 253                :    0.90
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:00.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP, t = 3           1.0e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35915
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 3                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 4                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 6                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 9                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5452
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4261
 p-value of test no 14                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 16                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4455
 p-value of test no 17                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 18                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.57
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.28
 p-value of test no 28                 :    0.95
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 33                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 35                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    1.78
 p-value of test no 36                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    3.03
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 42                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.64
 p-value of test no 46                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.13
 p-value of test no 47                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.14
 p-value of test no 48                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.68
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.95
 p-value of test no 50                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.43
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.64
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.43
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.91
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  488.50
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.64
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7234.85
 p-value of test no 57                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 59                 :    0.82
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 60                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.62
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.12
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.47
 p-value of test no 66                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.52
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5070.03
 p-value of test no 68                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45629
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869629
   j =  1                              :        399908747
   j =  2                              :            45619
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45837
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869837
   j =  1                              :        399908327
   j =  2                              :            45835
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 73                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 76                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 78                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.62
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 92                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
 p-value of test no 93                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.67
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 98                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 99                 :    0.9910
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 100                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 104                :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 105                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 106                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 107                :    0.74
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 108                :    0.9983
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
 p-value of test no 109                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 115                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 116                :    0.9914
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 117                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.49
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.45
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.48
 p-value of test no 122                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.18
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.40
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 128                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.87
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.62
 p-value of test no 133                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.54
 p-value of test no 134                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.58
 p-value of test no 135                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 140                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  160.60
 p-value of test no 141                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 142                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.13
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17721.10
 p-value of test no 145                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   15.65
 p-value of test no 146                :    0.9987
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.66
 p-value of test no 147                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.00
 p-value of test no 148                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.66
 p-value of test no 149                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.51
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.16
 p-value of test no 151                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.13
 p-value of test no 152                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.96
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.02
 p-value of test no 154                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.95
 p-value of test no 155                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.66
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.69
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  437.46
 p-value of test no 158                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  170.79
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  111.98
 p-value of test no 160                :  2.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.89
 p-value of test no 161                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.33
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  537.52
 p-value of test no 163                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.03
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.80
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.22
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.56
 p-value of test no 167                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.84
 p-value of test no 168                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.52
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.00
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.71
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  348.14
 p-value of test no 172                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.97
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.50
 p-value of test no 174                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.96
 p-value of test no 175                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.23
 p-value of test no 176                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.81
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    4.34
 p-value of test no 178                :    0.98
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.27
 p-value of test no 179                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.32
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    2.00
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.59
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    0.61
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
 p-value of test no 194                :    0.83
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.74
 p-value of test no 196                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.05
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.87
 p-value of test no 203                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.41
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 206                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  239.24
 p-value of test no 207                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.75
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 210                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9881.16
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 214                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10110.39
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 216                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 217                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 219                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4740.56
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.66
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4868.11
 p-value of test no 226                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4178.91
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4267.58
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11694.12
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11910.13
 p-value of test no 230                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.40
 p-value of test no 231                :    0.69
 
 
 -----------------------------------------------
 Total number of bits:  8000003196
 
 Normal statistic for number of bits   :   0.025
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.48
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  7999955955
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 234                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 237                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 238                :    0.20
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.64
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 242                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.90
 p-value of test no 243                :    0.82
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 248                :    0.11
 
 Sample variance                       :    1.01
 p-value of test no 249                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.57
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 252                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 253                :    0.70
 
 Sample variance                       :    0.41
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:26.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35916
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 4                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 7                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 8                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 9                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 11                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5597
 p-value of test no 13                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 14                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7186
 p-value of test no 20                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 23                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 24                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     888
 p-value of test no 25                 :    0.65
 
 Stat. AD (mNP2)                       :    0.24
 p-value of test no 26                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 27                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.01
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 29                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 32                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     315
 p-value of test no 37                 :    0.20
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 42                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.99
 p-value of test no 45                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.81
 p-value of test no 46                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.49
 p-value of test no 47                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.14
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.36
 p-value of test no 49                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.02
 p-value of test no 50                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.75
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.13
 p-value of test no 52                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.52
 p-value of test no 53                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  264.09
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  399.72
 p-value of test no 55                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1391.53
 p-value of test no 56                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7061.85
 p-value of test no 57                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 58                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 59                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.29
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 63                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.09
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   83.98
 p-value of test no 65                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.00
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.60
 p-value of test no 67                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5087.85
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45739
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869739
   j =  1                              :        399908523
   j =  2                              :            45737
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45809
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869809
   j =  1                              :        399908383
   j =  2                              :            45807
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 77                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 79                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 92                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 105                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
 p-value of test no 109                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
 p-value of test no 112                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 114                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.71
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.77
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.77
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.36
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.73
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.76
 p-value of test no 123                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.47
 p-value of test no 124                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.44
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.39
 p-value of test no 129                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 131                :    0.38
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.26
 p-value of test no 133                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.64
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.17
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.46
 p-value of test no 136                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.41
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 144                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17518.99
 p-value of test no 145                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.35
 p-value of test no 146                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.07
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.40
 p-value of test no 148                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.55
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.85
 p-value of test no 150                :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.12
 p-value of test no 151                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.22
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.96
 p-value of test no 153                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.75
 p-value of test no 154                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.28
 p-value of test no 155                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.36
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.21
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.56
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.29
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   53.03
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.05
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.19
 p-value of test no 162                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.17
 p-value of test no 163                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.15
 p-value of test no 164                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.88
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.55
 p-value of test no 166                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.43
 p-value of test no 167                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.12
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  369.08
 p-value of test no 169                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.93
 p-value of test no 170                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.85
 p-value of test no 171                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.70
 p-value of test no 172                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5195.40
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.76
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.33
 p-value of test no 175                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.79
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 177                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.05
 p-value of test no 178                :    0.09
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.41
 p-value of test no 179                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 180                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 182                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.80
 p-value of test no 183                :    0.21
 
 Sample variance                       :    0.81
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 187                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.11
 p-value of test no 188                :    0.87
 
 Sample variance                       :    1.06
 p-value of test no 189                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
 p-value of test no 190                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.39
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 195                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.85
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.41
 p-value of test no 198                :    0.82
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.34
 p-value of test no 203                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.76
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 206                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.14
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 210                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10056.97
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 213                :  3.1e-3
 
 Anderson-Darling statistic = A2       :    3.30
 p-value of test no 214                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10269.21
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.13
 p-value of test no 216                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.53
 p-value of test no 217                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 218                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 219                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 220                :    0.13
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.91
 p-value of test no 222                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 225                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4903.49
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.59
 p-value of test no 227                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.30
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11735.43
 p-value of test no 229                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.66
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.47
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000053275
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.72
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999992792
 
 Normal statistic for number of bits   :  -0.057
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 235                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.53
 p-value of test no 236                :  2.0e-3
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 237                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.46
 p-value of test no 238                :  7.0e-3
 
 Sample variance                       :    0.42
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 241                :    0.93
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 243                :    0.86
 
 Sample variance                       :    0.86
 p-value of test no 244                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.33
 p-value of test no 248                :    0.37
 
 Sample variance                       :    0.73
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.37
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 253                :    0.28
 
 Sample variance                       :    1.11
 p-value of test no 254                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:23.98
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35917
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 10                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 11                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 12                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5539
 p-value of test no 13                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4262
 p-value of test no 16                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7254
 p-value of test no 21                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 22                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.99
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 24                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     914
 p-value of test no 25                 :    0.32
 
 Stat. AD (mNP2)                       :    1.31
 p-value of test no 26                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.76
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.20
 p-value of test no 28                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    1.66
 p-value of test no 30                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     604
 p-value of test no 31                 :    0.44
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.28
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 38                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    2.72
 p-value of test no 45                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.01
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.18
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.85
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.72
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.17
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.88
 p-value of test no 51                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.31
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.20
 p-value of test no 53                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.14
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  469.54
 p-value of test no 55                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.31
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6953.45
 p-value of test no 57                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 59                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 60                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.47
 p-value of test no 61                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   66.53
 p-value of test no 65                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   11.27
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.65
 p-value of test no 67                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5185.48
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45885
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869885
   j =  1                              :        399908234
   j =  2                              :            45877
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45898
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869898
   j =  1                              :        399908208
   j =  2                              :            45890
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 72                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 77                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 85                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 88                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 91                 :    0.68
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 95                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.05
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 102                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 105                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 107                :    0.71
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 108                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 110                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.01
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 118                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.91
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.65
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.43
 p-value of test no 121                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.30
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.36
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.76
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.43
 p-value of test no 125                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 127                :    0.98
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   28.25
 p-value of test no 129                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 130                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 132                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.04
 p-value of test no 133                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.68
 p-value of test no 134                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.50
 p-value of test no 135                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 136                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 140                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.47
 p-value of test no 141                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 143                :    0.91
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17178.05
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.37
 p-value of test no 146                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.35
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.21
 p-value of test no 148                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.62
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.42
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.35
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.20
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.27
 p-value of test no 153                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.03
 p-value of test no 154                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.06
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.55
 p-value of test no 156                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.22
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  460.37
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  159.91
 p-value of test no 159                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.22
 p-value of test no 160                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.35
 p-value of test no 161                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.70
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.28
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  168.11
 p-value of test no 164                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.85
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.52
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.69
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4887.01
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.43
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  212.34
 p-value of test no 170                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.64
 p-value of test no 171                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.17
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5036.22
 p-value of test no 173                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  330.16
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.27
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.47
 p-value of test no 176                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.90
 p-value of test no 177                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.45
 p-value of test no 178                :    0.22
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 179                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 182                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 183                :    0.70
 
 Sample variance                       :    1.67
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 185                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 187                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 188                :    0.22
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
 p-value of test no 191                :    0.56
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 192                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
 p-value of test no 193                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.71
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.00
 p-value of test no 198                :    0.27
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 201                :    0.11
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 202                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.44
 p-value of test no 203                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.64
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 206                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.21
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 208                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.13
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9867.96
 p-value of test no 215                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.32
 p-value of test no 216                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 220                :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4790.01
 p-value of test no 222                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.74
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 225                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.39
 p-value of test no 226                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4166.27
 p-value of test no 227                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4264.56
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11865.01
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.94
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.20
 p-value of test no 231                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  7999991511
 
 Normal statistic for number of bits   :  -0.067
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   75.24
 p-value of test no 233                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  8000068263
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 238                :    0.40
 
 Sample variance                       :    1.12
 p-value of test no 239                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 240                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 242                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 243                :    0.10
 
 Sample variance                       :    2.44
 p-value of test no 244                :  9.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.86
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.77
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.04
 p-value of test no 254                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:32.80
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35918
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 3                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 4                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 7                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 8                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 11                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 12                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5406
 p-value of test no 13                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4477
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7366
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 20                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7400
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 22                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 23                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 24                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     962
 p-value of test no 25                 :    0.02
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 26                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.39
 p-value of test no 27                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.00
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 34                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    0.10
 p-value of test no 36                 : 1 -  3.7e-5    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.60
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 42                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 44                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 45                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 47                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.94
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.99
 p-value of test no 49                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.99
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.54
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.87
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.62
 p-value of test no 53                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  266.54
 p-value of test no 54                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.75
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1471.77
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7053.59
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.92
 p-value of test no 61                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.89
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.41
 p-value of test no 66                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.65
 p-value of test no 67                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.79
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907843
   j =  2                              :            46074
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45740
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869740
   j =  1                              :        399908523
   j =  2                              :            45734
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 73                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 80                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 81                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 91                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 97                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 102                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.35
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 105                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 108                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 6.02e-5
 p-value of test no 113                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 118                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.83
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.28
 p-value of test no 120                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.34
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.74
 p-value of test no 122                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.41
 p-value of test no 123                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.68
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.38
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.71
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 128                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.89
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 130                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.35
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.65
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.24
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 136                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.76
 p-value of test no 137                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.93
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 143                :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17502.74
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.62
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.71
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.73
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.13
 p-value of test no 149                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.74
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.53
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.74
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.63
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.20
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.26
 p-value of test no 155                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.78
 p-value of test no 156                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.20
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.91
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.46
 p-value of test no 159                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.38
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.29
 p-value of test no 161                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  125.72
 p-value of test no 162                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  500.09
 p-value of test no 163                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  173.17
 p-value of test no 164                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.16
 p-value of test no 165                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.66
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.10
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.40
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.34
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.29
 p-value of test no 170                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.16
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.75
 p-value of test no 172                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4994.51
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  419.47
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  233.20
 p-value of test no 175                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.08
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.28
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.86
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.078
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.41
 p-value of test no 183                :    0.34
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 187                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
 p-value of test no 191                :    0.85
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.75
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.89
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9988
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.09
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.22
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 206                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.54
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.49
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.31
 p-value of test no 211                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.10
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 214                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10160.67
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.24
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 218                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 220                :    0.20
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 221                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4984.15
 p-value of test no 222                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4939.47
 p-value of test no 226                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.78
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.10
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12035.05
 p-value of test no 229                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12192.74
 p-value of test no 230                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.39
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999994577
 
 Normal statistic for number of bits   :  -0.043
 p-value of test no 232                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.74
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000101668
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.69
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 242                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.19
 p-value of test no 243                :    0.99
 
 Sample variance                       :    1.86
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 246                :    0.90
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.98
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    1.13
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:06.29
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  24  ClosePairs mNP1, t = 9         1 -  3.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35919
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 3                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 5                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 8                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 10                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 11                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 12                 :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 15                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:22.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 16                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 18                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7411
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7517
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.30
 p-value of test no 22                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 23                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 24                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.70
 p-value of test no 27                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.27
 p-value of test no 33                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 35                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.98
 p-value of test no 40                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     143
 p-value of test no 43                 :    0.70
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.07
 p-value of test no 46                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.17
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.26
 p-value of test no 48                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.78
 p-value of test no 49                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.63
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.70
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.50
 p-value of test no 53                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  209.02
 p-value of test no 54                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  361.49
 p-value of test no 55                 :    0.9952
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1390.48
 p-value of test no 56                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7060.39
 p-value of test no 57                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.72
 p-value of test no 61                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 63                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 64                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   52.68
 p-value of test no 65                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.65
 p-value of test no 66                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.20
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5036.30
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45334
 p-value of test no 70                 :    0.9946
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869334
   j =  1                              :        399909335
   j =  2                              :            45328
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45536
 p-value of test no 71                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869536
   j =  1                              :        399908931
   j =  2                              :            45530
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 74                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 76                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 88                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 91                 :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 92                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 93                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 94                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.81
 p-value of test no 95                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :  6.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 97                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 100                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 102                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.46
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.98e-5
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
 p-value of test no 110                :    0.18
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
 p-value of test no 113                :    0.73
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 114                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 116                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 117                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.25
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.49
 p-value of test no 120                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.45
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.83
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.07
 p-value of test no 123                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.82
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.28
 p-value of test no 125                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.93
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 130                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 132                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.62
 p-value of test no 133                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.12
 p-value of test no 135                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.91
 p-value of test no 136                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.66
 p-value of test no 137                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    3.29
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  173.85
 p-value of test no 141                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 143                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 144                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17218.08
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.44
 p-value of test no 146                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.30
 p-value of test no 147                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.39
 p-value of test no 148                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.18
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.85
 p-value of test no 150                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.75
 p-value of test no 151                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.53
 p-value of test no 152                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.14
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.09
 p-value of test no 154                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.19
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.03
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.35
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.12
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.46
 p-value of test no 159                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.31
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.13
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.97
 p-value of test no 162                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.20
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.75
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.36
 p-value of test no 165                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.56
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.88
 p-value of test no 167                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.01
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.41
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  217.39
 p-value of test no 170                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.84
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.79
 p-value of test no 172                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.26
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.17
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  161.16
 p-value of test no 175                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.65
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.66
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.56
 p-value of test no 179                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 181                :    0.93
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 182                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.61
 p-value of test no 183                :    0.73
 
 Sample variance                       :    1.33
 p-value of test no 184                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.87
 p-value of test no 189                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
 p-value of test no 191                :    0.86
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.07
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.00
 p-value of test no 198                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.60
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 205                :    0.38
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 206                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.58
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.50
 p-value of test no 208                :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
 p-value of test no 209                :    0.9969
 
 Anderson-Darling statistic = A2       :    4.91
 p-value of test no 210                :  3.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9570.81
 p-value of test no 211                :    0.9989
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 214                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9956.16
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.26
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 221                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4800.51
 p-value of test no 222                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 225                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4960.70
 p-value of test no 226                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4132.30
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4271.33
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11872.61
 p-value of test no 229                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.45
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.54
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000199933
 
 Normal statistic for number of bits   :    1.58
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.21
 p-value of test no 233                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000126226
 
 Normal statistic for number of bits   :    1.00
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.57
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 237                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.28
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 243                :    0.13
 
 Sample variance                       :    0.97
 p-value of test no 244                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 245                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 248                :    0.12
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.29
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 253                :    0.15
 
 Sample variance                       :    1.89
 p-value of test no 254                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:35.53
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35920
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 5                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997269
   j =  2                              :             1364
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:24.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 9                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:25.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 12                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5451
 p-value of test no 13                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 15                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:23.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 16                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7460
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7506
 p-value of test no 21                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 22                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.68
 p-value of test no 23                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    1.76
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    2.77
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 28                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 30                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     607
 p-value of test no 31                 :    0.39
 
 Stat. AD (mNP2)                       :    0.23
 p-value of test no 32                 :    0.98
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 33                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.06
 p-value of test no 34                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 35                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 36                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 38                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 39                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 40                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.25
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.13
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.66
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.09
 p-value of test no 48                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.77
 p-value of test no 49                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.23
 p-value of test no 50                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.52
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.86
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.88
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  262.78
 p-value of test no 54                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.34
 p-value of test no 55                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1476.08
 p-value of test no 56                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6978.24
 p-value of test no 57                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.03
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 64                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.33
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.12
 p-value of test no 67                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5111.49
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46131
 p-value of test no 70                 :    0.12
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870131
   j =  1                              :        399907740
   j =  2                              :            46127
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45474
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869474
   j =  1                              :        399909055
   j =  2                              :            45468
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 77                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 80                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 85                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 88                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 97                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 98                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 99                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 101                :    0.76
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 102                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.10
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 105                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 108                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 111                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.33
 p-value of test no 115                :    0.9900
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.90
 p-value of test no 116                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.99
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.28
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.90
 p-value of test no 120                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.64
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.19
 p-value of test no 122                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.87
 p-value of test no 123                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.58
 p-value of test no 124                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.93
 p-value of test no 125                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.18
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.51
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.70
 p-value of test no 133                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.14
 p-value of test no 134                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.22
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.97
 p-value of test no 141                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.36
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.74
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.86
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.39
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   42.12
 p-value of test no 149                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.27
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.38
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.90
 p-value of test no 152                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.24
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.34
 p-value of test no 154                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.54
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.10
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.07
 p-value of test no 157                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  448.94
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.53
 p-value of test no 159                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.92
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.06
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.35
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  513.85
 p-value of test no 163                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.04
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.14
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.53
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.76
 p-value of test no 167                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.49
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.84
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.79
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.49
 p-value of test no 171                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  436.21
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4882.49
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.02
 p-value of test no 174                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.32
 p-value of test no 175                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.52
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.20
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 182                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.13
 p-value of test no 184                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 186                :    0.70
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 187                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
 p-value of test no 193                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    : 4.33e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 195                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.98
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.24
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 200                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.35
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.86
 p-value of test no 203                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.13
 p-value of test no 207                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9917.76
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 213                :    0.82
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 214                :    0.9979
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9990.46
 p-value of test no 215                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 216                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.083
 p-value of test no 218                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4804.73
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5005.61
 p-value of test no 226                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.03
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4157.38
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.86
 p-value of test no 229                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.13
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.83
 p-value of test no 231                :    0.24
 
 
 -----------------------------------------------
 Total number of bits:  8000104725
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.81
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  7999836441
 
 Normal statistic for number of bits   :   -1.29
 p-value of test no 234                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 236                :    0.92
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 237                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.75
 
 Sample variance                       :    0.89
 p-value of test no 239                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 240                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.23
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 243                :    0.17
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.70
 p-value of test no 249                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 250                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 252                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.52
 p-value of test no 253                :    0.94
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:40.47
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35921
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 3                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 6                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 7                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 9                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 10                 :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 11                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5491
 p-value of test no 13                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 15                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4471
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 18                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 19                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 21                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 23                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     861
 p-value of test no 25                 :    0.90
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 28                 :    0.70
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.59
 p-value of test no 32                 :    0.66
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 38                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    1.22
 p-value of test no 39                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.21
 p-value of test no 40                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 41                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 42                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 44                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.75
 p-value of test no 46                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.26
 p-value of test no 47                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.31
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.02
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.18
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.62
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.67
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   79.85
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.59
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  423.80
 p-value of test no 55                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.39
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6744.38
 p-value of test no 57                 :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.24
 p-value of test no 61                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 62                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 64                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.80
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.84
 p-value of test no 66                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   77.68
 p-value of test no 67                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4980.39
 p-value of test no 68                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46007
 p-value of test no 70                 :    0.28
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870007
   j =  1                              :        399907990
   j =  2                              :            45999
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45485
 p-value of test no 71                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869485
   j =  1                              :        399909035
   j =  2                              :            45475
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
 p-value of test no 72                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 80                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 83                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 88                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 92                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 93                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 104                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 105                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 106                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 107                :    0.66
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
 p-value of test no 109                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 118                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.50
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.33
 p-value of test no 120                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.83
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.16
 p-value of test no 123                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.95
 p-value of test no 124                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.23
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 127                :    0.16
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.95
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 130                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 132                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.79
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.98
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.57
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.35
 p-value of test no 136                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.38
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 143                :    0.85
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 144                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17174.35
 p-value of test no 145                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.08
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.35
 p-value of test no 147                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.49
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.17
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    7.77
 p-value of test no 150                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.76
 p-value of test no 151                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.64
 p-value of test no 152                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.97
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   44.39
 p-value of test no 154                :  6.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.55
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.36
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.57
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  475.86
 p-value of test no 158                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.37
 p-value of test no 159                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.69
 p-value of test no 160                :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.41
 p-value of test no 161                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.28
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.33
 p-value of test no 163                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.87
 p-value of test no 164                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.66
 p-value of test no 165                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.97
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.40
 p-value of test no 167                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.45
 p-value of test no 168                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.95
 p-value of test no 169                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.59
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.19
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.45
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4971.12
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.91
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.43
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.57
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.50
 p-value of test no 177                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.73
 p-value of test no 178                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.02
 p-value of test no 179                :    0.15
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 180                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 183                :    0.75
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 185                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 3.37e-3
 p-value of test no 191                :    0.91
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 192                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
 p-value of test no 193                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.58
 p-value of test no 196                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   26.93
 p-value of test no 198                :  7.3e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.50
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 204                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  211.89
 p-value of test no 207                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9938.95
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.23
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 214                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.84
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.10
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.55
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4864.78
 p-value of test no 222                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 225                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4909.39
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4180.72
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.33
 p-value of test no 228                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.76
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11407.07
 p-value of test no 230                :    0.9970
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.99
 p-value of test no 231                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000062821
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.45
 p-value of test no 233                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  7999883691
 
 Normal statistic for number of bits   :   -0.92
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    0.85
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.11
 p-value of test no 244                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.58
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.48
 p-value of test no 249                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 250                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:12.50
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  87  LongestHeadRun, r = 27          7.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35922
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 5                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1273
 p-value of test no 9                  :    0.9934
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334393
   j =  1                              :        599997454
   j =  2                              :             1273
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1460
 p-value of test no 10                 :  5.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334580
   j =  1                              :        599997080
   j =  2                              :             1460
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 12                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5383
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 15                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4366
 p-value of test no 17                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7329
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7159
 p-value of test no 19                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.61
 p-value of test no 23                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 24                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     916
 p-value of test no 25                 :    0.30
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 26                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 27                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.16
 p-value of test no 28                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.11
 p-value of test no 29                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     573
 p-value of test no 31                 :    0.86
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.47
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.62
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 41                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 42                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.99
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.51
 p-value of test no 48                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.37
 p-value of test no 49                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.14
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.07
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.60
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.39
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.70
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.60
 p-value of test no 55                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.02
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7101.09
 p-value of test no 57                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 59                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 60                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.68
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.30
 p-value of test no 65                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.20
 p-value of test no 66                 :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  123.21
 p-value of test no 67                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4911.25
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46197
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870197
   j =  1                              :        399907609
   j =  2                              :            46191
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46286
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870286
   j =  1                              :        399907429
   j =  2                              :            46284
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 72                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 76                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 79                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 81                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 85                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 93                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 98                 :  9.5e-3
 
 Anderson-Darling statistic = A2       :    3.57
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
 p-value of test no 101                :    0.9985
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 105                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 107                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
 p-value of test no 109                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
 p-value of test no 110                :    0.27
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
 p-value of test no 112                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.86
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 118                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.19
 p-value of test no 119                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.69
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.21
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.24
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.22
 p-value of test no 123                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.41
 p-value of test no 124                :  3.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.51
 p-value of test no 125                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.75
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.52
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.01
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.36
 p-value of test no 135                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.010
 p-value of test no 137                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.25
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.89
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17183.94
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.69
 p-value of test no 146                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.17
 p-value of test no 147                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.56
 p-value of test no 148                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.88
 p-value of test no 149                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.79
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.26
 p-value of test no 151                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.43
 p-value of test no 152                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.03
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.81
 p-value of test no 154                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.57
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.95
 p-value of test no 156                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.25
 p-value of test no 157                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.71
 p-value of test no 158                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.34
 p-value of test no 159                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.23
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.46
 p-value of test no 161                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.34
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.01
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.39
 p-value of test no 164                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.29
 p-value of test no 165                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.30
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.41
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5052.77
 p-value of test no 168                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  434.78
 p-value of test no 169                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.53
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.21
 p-value of test no 171                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.07
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4881.26
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  352.63
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.35
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.86
 p-value of test no 176                :    0.38
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.00
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.27
 p-value of test no 179                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 180                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 187                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.41
 p-value of test no 189                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
 p-value of test no 190                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 192                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.97
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.59
 p-value of test no 198                :    0.09
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.75
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 202                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.73
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.53
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.28
 p-value of test no 207                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 209                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 210                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.15
 p-value of test no 211                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 213                :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9774.47
 p-value of test no 215                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.086
 p-value of test no 218                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 219                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.76
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.39
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.33
 p-value of test no 226                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.34
 p-value of test no 227                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.76
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.07
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11883.22
 p-value of test no 230                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.70
 p-value of test no 231                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  7999741236
 
 Normal statistic for number of bits   :   -2.05
 p-value of test no 232                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.40
 p-value of test no 233                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000286588
 
 Normal statistic for number of bits   :    2.27
 p-value of test no 234                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 237                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 238                :    0.23
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 240                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 241                :    0.82
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.43
 p-value of test no 243                :    0.92
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-3
 p-value of test no 245                :    0.9988
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 247                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.94
 p-value of test no 248                :    0.03
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.70
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.95
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:42.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  40  Permutation, t = 3              0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35923
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 6                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 8                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5311
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4337
 p-value of test no 14                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7434
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4316
 p-value of test no 16                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4358
 p-value of test no 17                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 18                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7217
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.81
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    4.32
 p-value of test no 23                 :  6.2e-3
 
 Test on the Nm values of W_{n,i}(mNP1):    1.72
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 26                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 28                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.82
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     567
 p-value of test no 31                 :    0.91
 
 Stat. AD (mNP2)                       :    2.63
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 33                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.77
 p-value of test no 34                 :    0.50
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.16
 p-value of test no 36                 :    0.9972
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 38                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 44                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.77
 p-value of test no 46                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 47                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.01
 p-value of test no 48                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.05
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.56
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.03
 p-value of test no 51                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.91
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.01
 p-value of test no 54                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.59
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1426.49
 p-value of test no 56                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7088.41
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.15
 p-value of test no 61                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.52e-3
 p-value of test no 62                 :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  4.6e-3
 
 Anderson-Darling statistic = A2       :    5.57
 p-value of test no 64                 :  1.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  101.79
 p-value of test no 65                 :  6.1e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   14.27
 p-value of test no 66                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.57
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.61
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46171
 p-value of test no 70                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870171
   j =  1                              :        399907661
   j =  2                              :            46165
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45541
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869541
   j =  1                              :        399908920
   j =  2                              :            45537
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 73                 :    0.07
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 76                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 79                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 80                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 84                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 91                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 94                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.38
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 97                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 99                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 101                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 103                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 105                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 108                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.85e-5
 p-value of test no 109                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 3.45e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 114                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    3.01
 p-value of test no 115                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 116                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.48
 p-value of test no 118                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.64
 p-value of test no 119                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   86.89
 p-value of test no 120                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.43
 p-value of test no 121                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.27
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.73
 p-value of test no 123                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.57
 p-value of test no 124                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.94
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.75
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.48
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.44
 p-value of test no 133                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.99
 p-value of test no 134                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.44
 p-value of test no 135                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.56
 p-value of test no 136                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.57
 p-value of test no 137                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 138                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.80
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 144                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17352.68
 p-value of test no 145                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   54.85
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.61
 p-value of test no 147                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.06
 p-value of test no 148                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.74
 p-value of test no 149                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.41
 p-value of test no 150                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.58
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.47
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.88
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.87
 p-value of test no 154                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.30
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.50
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.57
 p-value of test no 157                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.03
 p-value of test no 158                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.71
 p-value of test no 159                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.05
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.17
 p-value of test no 161                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.18
 p-value of test no 162                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.14
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.94
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.12
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.22
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  432.60
 p-value of test no 167                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5134.46
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  334.27
 p-value of test no 169                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.84
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.07
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.28
 p-value of test no 172                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4892.24
 p-value of test no 173                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.82
 p-value of test no 174                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.45
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.63
 p-value of test no 176                :    0.40
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.38
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.12
 p-value of test no 179                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 180                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.40
 p-value of test no 183                :    0.92
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 187                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 188                :    0.46
 
 Sample variance                       :    1.82
 p-value of test no 189                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
 p-value of test no 194                :    0.76
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 195                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.21
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.89
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 200                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  198.07
 p-value of test no 203                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.06
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 208                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 209                :    0.12
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 210                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10177.89
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9958.67
 p-value of test no 215                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 221                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.26
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 225                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5001.03
 p-value of test no 226                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4232.12
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4165.72
 p-value of test no 228                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11750.00
 p-value of test no 229                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11733.97
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.38
 p-value of test no 231                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000124906
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.94
 p-value of test no 233                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000154444
 
 Normal statistic for number of bits   :    1.22
 p-value of test no 234                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.40
 p-value of test no 239                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.40
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 243                :    0.32
 
 Sample variance                       :    0.42
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 245                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.64
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.80
 p-value of test no 248                :    0.79
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.05
 p-value of test no 253                :    0.15
 
 Sample variance                       :    0.39
 p-value of test no 254                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.45
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:37.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     6.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35924
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 3                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 4                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 5                  :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 6                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 8                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 9                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 10                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 11                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5415
 p-value of test no 13                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4213
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4247
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4271
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7381
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.83
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 23                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     894
 p-value of test no 25                 :    0.57
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.08
 p-value of test no 29                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.31
 p-value of test no 30                 :    0.23
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.90
 p-value of test no 33                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 38                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    0.28
 p-value of test no 39                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 42                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.50
 p-value of test no 45                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.32
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.64
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.11
 p-value of test no 49                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.47
 p-value of test no 50                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.16
 p-value of test no 51                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.52
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.36
 p-value of test no 53                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.44
 p-value of test no 54                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.67
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1454.05
 p-value of test no 56                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6938.49
 p-value of test no 57                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 60                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.93
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   75.55
 p-value of test no 65                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.99
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  118.23
 p-value of test no 67                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.66
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45771
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869771
   j =  1                              :        399908462
   j =  2                              :            45763
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45648
 p-value of test no 71                 :    0.86
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869648
   j =  1                              :        399908706
   j =  2                              :            45644
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 72                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 76                 :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 77                 :    0.72
 
 Anderson-Darling statistic = A2       :    3.23
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 79                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 81                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 87                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 88                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 92                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 95                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 97                 :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
 p-value of test no 98                 :    0.9909
 
 Anderson-Darling statistic = A2       :    4.06
 p-value of test no 99                 :  8.3e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 100                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 102                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 105                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
 p-value of test no 110                :    0.91
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 111                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
 p-value of test no 112                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
 p-value of test no 113                :    0.20
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 114                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 117                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.38
 p-value of test no 118                :    0.9913
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.79
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.41
 p-value of test no 120                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.75
 p-value of test no 121                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.69
 p-value of test no 122                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.46
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   54.32
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.74
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 128                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.77
 p-value of test no 129                :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 130                :  4.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
 p-value of test no 131                :    0.9924
 
 Anderson-Darling statistic = A2       :    5.22
 p-value of test no 132                :  2.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   16.97
 p-value of test no 133                :    0.9995    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.67
 p-value of test no 134                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.93
 p-value of test no 135                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.98
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 139                :    0.77
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 140                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.59
 p-value of test no 141                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 142                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 144                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17052.74
 p-value of test no 145                :    0.98
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.26
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.84
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.35
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.89
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.57
 p-value of test no 150                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.13
 p-value of test no 151                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.94
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.07
 p-value of test no 153                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.23
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.84
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.91
 p-value of test no 156                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.48
 p-value of test no 157                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  483.76
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.12
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.27
 p-value of test no 160                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.98
 p-value of test no 161                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.36
 p-value of test no 162                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.14
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.07
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.99
 p-value of test no 165                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.17
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.99
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.90
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.71
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.13
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  344.35
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  340.26
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4946.41
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.18
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.49
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.91
 p-value of test no 176                :    0.03
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.89
 p-value of test no 177                :  1.9e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.65
 p-value of test no 178                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.70
 p-value of test no 179                :    0.9966
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 180                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 182                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 183                :    0.26
 
 Sample variance                       :    2.43
 p-value of test no 184                :  9.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 187                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 188                :    0.25
 
 Sample variance                       :    1.02
 p-value of test no 189                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.20
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.11
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.40
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.07
 p-value of test no 198                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 200                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  230.41
 p-value of test no 203                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 206                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.93
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 208                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.20
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 210                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10114.22
 p-value of test no 211                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 212                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.22
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10207.02
 p-value of test no 215                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.81
 p-value of test no 216                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.83e-3
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 221                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4818.16
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 223                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 224                :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4989.01
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.48
 p-value of test no 227                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3980.42
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11707.11
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11802.10
 p-value of test no 230                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.18
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000136153
 
 Normal statistic for number of bits   :    1.08
 p-value of test no 232                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.05
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999856613
 
 Normal statistic for number of bits   :   -1.13
 p-value of test no 234                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 235                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 236                :  2.5e-3
 
 Anderson-Darling statistic = A2       :    4.40
 p-value of test no 237                :  5.8e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.39
 p-value of test no 238                :  8.4e-3
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 241                :    0.17
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 242                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.91
 p-value of test no 244                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.54
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 248                :    0.61
 
 Sample variance                       :    0.44
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 250                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.71
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.38
 p-value of test no 253                :    0.92
 
 Sample variance                       :    0.66
 p-value of test no 254                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:01.59
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  67  MatrixRank, L=30, r=26          0.9995 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35925
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 4                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 6                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 7                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 9                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 12                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5455
 p-value of test no 13                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 14                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7276
 p-value of test no 15                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 16                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4511
 p-value of test no 17                 :  4.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7129
 p-value of test no 18                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7178
 p-value of test no 19                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.95
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     919
 p-value of test no 25                 :    0.27
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 27                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 30                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    3.92
 p-value of test no 33                 :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 36                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    1.77
 p-value of test no 38                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    1.64
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.74
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 45                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.35
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.24
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.83
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.72
 p-value of test no 50                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   68.85
 p-value of test no 51                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.54
 p-value of test no 52                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.84
 p-value of test no 53                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  197.70
 p-value of test no 54                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  460.49
 p-value of test no 55                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1350.12
 p-value of test no 56                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7145.06
 p-value of test no 57                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 60                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.82
 p-value of test no 61                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.12
 p-value of test no 65                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.38
 p-value of test no 66                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.47
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.16
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908230
   j =  2                              :            45882
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45841
 p-value of test no 71                 :    0.57
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869841
   j =  1                              :        399908320
   j =  2                              :            45837
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 76                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 84                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 85                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 88                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 91                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 95                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
 p-value of test no 112                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
 p-value of test no 113                :    0.90
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.66
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.40
 p-value of test no 117                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.51
 p-value of test no 119                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.82
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.34
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.05
 p-value of test no 122                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.77
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.94
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.36
 p-value of test no 125                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 127                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.76
 p-value of test no 129                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 130                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.12
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.49
 p-value of test no 134                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.37
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.70
 p-value of test no 141                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17426.57
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.89
 p-value of test no 146                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.19
 p-value of test no 147                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.86
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.46
 p-value of test no 149                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.83
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.40
 p-value of test no 151                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.98
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.81
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.21
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.78
 p-value of test no 155                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.84
 p-value of test no 156                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.96
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.29
 p-value of test no 158                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  141.63
 p-value of test no 159                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.35
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.11
 p-value of test no 161                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.66
 p-value of test no 162                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  442.79
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.29
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.41
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.39
 p-value of test no 166                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.70
 p-value of test no 167                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4712.96
 p-value of test no 168                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  343.62
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.46
 p-value of test no 170                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.53
 p-value of test no 171                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.04
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5005.12
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.55
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.97
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.75
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.03
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.14
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.44
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.082
 p-value of test no 183                :    0.47
 
 Sample variance                       :    0.57
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 186                :    0.37
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 187                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 188                :    0.46
 
 Sample variance                       :    0.94
 p-value of test no 189                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 192                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
 p-value of test no 193                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 195                :    0.9972
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.50
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.77
 p-value of test no 198                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.73
 p-value of test no 203                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.61
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10091.15
 p-value of test no 211                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 214                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9954.50
 p-value of test no 215                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 216                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.59
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 219                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 221                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4829.20
 p-value of test no 222                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 223                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 225                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4786.13
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4274.74
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.63
 p-value of test no 228                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11577.69
 p-value of test no 229                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11734.59
 p-value of test no 230                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.53
 p-value of test no 231                :    0.68
 
 
 -----------------------------------------------
 Total number of bits:  8000019477
 
 Normal statistic for number of bits   :    0.15
 p-value of test no 232                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.37
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000139951
 
 Normal statistic for number of bits   :    1.11
 p-value of test no 234                :    0.13
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 236                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.025
 p-value of test no 238                :    0.51
 
 Sample variance                       :    0.80
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 240                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.73
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.46
 p-value of test no 244                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 245                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.28
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 247                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.21
 p-value of test no 248                :    0.11
 
 Sample variance                       :    0.74
 p-value of test no 249                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 250                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 252                :    0.9925
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.20
 p-value of test no 253                :    0.42
 
 Sample variance                       :    1.06
 p-value of test no 254                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:30.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35926
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 3                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 4                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 5                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 6                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 8                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 9                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 10                 :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5454
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4374
 p-value of test no 14                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 15                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4506
 p-value of test no 16                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4490
 p-value of test no 17                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7335
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 19                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7409
 p-value of test no 20                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 21                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 23                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     897
 p-value of test no 25                 :    0.53
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 29                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 30                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 32                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.06
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.64
 p-value of test no 35                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 36                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     308
 p-value of test no 37                 :    0.33
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 38                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 39                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.07
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     120
 p-value of test no 43                 :    0.9934
 
 Stat. AD (mNP2)                       :    1.87
 p-value of test no 44                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 45                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.11
 p-value of test no 46                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 47                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   31.75
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.03
 p-value of test no 49                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.38
 p-value of test no 50                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.61
 p-value of test no 51                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.60
 p-value of test no 52                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.24
 p-value of test no 53                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  231.50
 p-value of test no 54                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  467.84
 p-value of test no 55                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1343.44
 p-value of test no 56                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6926.41
 p-value of test no 57                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 60                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.35
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.79
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.84
 p-value of test no 66                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.35
 p-value of test no 67                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5051.98
 p-value of test no 68                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45762
 p-value of test no 70                 :    0.71
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869762
   j =  1                              :        399908479
   j =  2                              :            45756
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45705
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869705
   j =  1                              :        399908595
   j =  2                              :            45695
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 72                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 76                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 90                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 92                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 95                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.11
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 97                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 99                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 101                :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 105                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.44
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 110                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.55e-5
 p-value of test no 112                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
 p-value of test no 113                :    0.04
 
 Anderson-Darling statistic = A2       :    2.57
 p-value of test no 114                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 115                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 116                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.44
 p-value of test no 117                :  7.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.31
 p-value of test no 119                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   88.24
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.14
 p-value of test no 121                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   56.68
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.19
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.75
 p-value of test no 125                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 127                :    0.25
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 128                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.34
 p-value of test no 129                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 130                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.30
 p-value of test no 133                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.97
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.98
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.22
 p-value of test no 136                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 140                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.43
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17711.54
 p-value of test no 145                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.70
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.35
 p-value of test no 147                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.44
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.39
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.35
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.37
 p-value of test no 151                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.14
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.20
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.08
 p-value of test no 154                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.31
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.36
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.19
 p-value of test no 157                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.72
 p-value of test no 158                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  122.15
 p-value of test no 159                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.04
 p-value of test no 160                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.89
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.69
 p-value of test no 162                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  453.76
 p-value of test no 163                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.80
 p-value of test no 164                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.27
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.10
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.35
 p-value of test no 167                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.50
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  422.67
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.17
 p-value of test no 170                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.23
 p-value of test no 171                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.61
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.25
 p-value of test no 173                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.07
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.79
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.97
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.100
 p-value of test no 177                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.70
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.082
 p-value of test no 179                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 182                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 185                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.10
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 187                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 188                :    0.11
 
 Sample variance                       :    0.63
 p-value of test no 189                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
 p-value of test no 191                :    0.82
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
 p-value of test no 193                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 195                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.49
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.30
 p-value of test no 198                :    0.73
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.96
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 206                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.75
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:58.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9965.75
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 213                :    0.04
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10199.60
 p-value of test no 215                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.066
 p-value of test no 216                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.21
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 221                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4794.80
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 223                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 224                :    0.94
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 225                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4734.15
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4092.63
 p-value of test no 227                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3977.88
 p-value of test no 228                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11717.23
 p-value of test no 229                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11751.11
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.42
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000050716
 
 Normal statistic for number of bits   :    0.40
 p-value of test no 232                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.04
 p-value of test no 233                :    0.47
 
 
 -----------------------------------------------
 Total number of bits:  8000134758
 
 Normal statistic for number of bits   :    1.07
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.35
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 238                :    0.28
 
 Sample variance                       :    0.76
 p-value of test no 239                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 240                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.50
 p-value of test no 244                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 246                :    0.27
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.30
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 252                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 253                :    0.12
 
 Sample variance                       :    1.02
 p-value of test no 254                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:15.64
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35927
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1284
 p-value of test no 3                  :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334404
   j =  1                              :        599997432
   j =  2                              :             1284
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 4                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 8                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 10                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 12                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5282
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 18                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 19                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 21                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 22                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.74
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    2.27
 p-value of test no 27                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 28                 :    0.9943
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 30                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     618
 p-value of test no 31                 :    0.24
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.21
 p-value of test no 35                 :    0.26
 
 Test on the Nm values of W_{n,i}(mNP1):    1.63
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    1.28
 p-value of test no 39                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.24
 p-value of test no 41                 :    0.25
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 42                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     163
 p-value of test no 43                 :    0.15
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 44                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 45                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.51
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 47                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.64
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.33
 p-value of test no 49                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.59
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.53
 p-value of test no 51                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.26
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.70
 p-value of test no 53                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.43
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.39
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1353.10
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.15
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 58                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 59                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.28
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 64                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.61
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.66
 p-value of test no 66                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.66
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5112.00
 p-value of test no 68                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46119
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870119
   j =  1                              :        399907763
   j =  2                              :            46117
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907874
   j =  2                              :            46060
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.38
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 80                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 83                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 87                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 92                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 98                 :  3.6e-3
 
 Anderson-Darling statistic = A2       :    4.26
 p-value of test no 99                 :  6.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 101                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 104                :    0.85
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 106                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 108                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
 p-value of test no 109                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
 p-value of test no 110                :    0.20
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
 p-value of test no 112                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 113                :    0.24
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 116                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 118                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.44
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.71
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.40
 p-value of test no 121                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.24
 p-value of test no 122                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.21
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.95
 p-value of test no 124                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.37
 p-value of test no 125                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.41
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 128                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.51
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 130                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.82
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.82
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.42
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 140                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.27
 p-value of test no 141                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 142                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 143                :    0.89
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 144                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17184.74
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   50.52
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.59
 p-value of test no 147                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.44
 p-value of test no 148                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.13
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.06
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.40
 p-value of test no 151                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.41
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.10
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.28
 p-value of test no 154                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.20
 p-value of test no 155                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.34
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.11
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  464.77
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.48
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.87
 p-value of test no 160                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.25
 p-value of test no 161                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.30
 p-value of test no 162                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.97
 p-value of test no 163                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.38
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.48
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  329.52
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.32
 p-value of test no 167                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5034.86
 p-value of test no 168                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.11
 p-value of test no 169                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.73
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  409.05
 p-value of test no 171                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.01
 p-value of test no 172                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5022.20
 p-value of test no 173                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.77
 p-value of test no 174                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.25
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.09
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.99
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.71
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.74
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 188                :    0.65
 
 Sample variance                       :    1.11
 p-value of test no 189                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
 p-value of test no 190                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 191                :    0.64
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
 p-value of test no 193                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.39
 p-value of test no 196                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.76
 p-value of test no 198                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.45
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 205                :    0.10
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  241.31
 p-value of test no 207                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9915.91
 p-value of test no 211                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 214                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.92
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 216                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 218                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.18
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 223                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4743.91
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.80
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.16
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11823.46
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11710.00
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.75
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000094495
 
 Normal statistic for number of bits   :    0.75
 p-value of test no 232                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.67
 p-value of test no 233                :    0.64
 
 
 -----------------------------------------------
 Total number of bits:  7999937547
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.044
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.58
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.37
 p-value of test no 244                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.51
 p-value of test no 246                :  3.3e-3
 
 Anderson-Darling statistic = A2       :    2.61
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 248                :    0.06
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 253                :    0.34
 
 Sample variance                       :    0.79
 p-value of test no 254                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.85
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:31.04
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35928
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 5                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 7                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 8                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 9                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 10                 :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5482
 p-value of test no 13                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 14                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7270
 p-value of test no 15                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 16                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4296
 p-value of test no 17                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 19                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7570
 p-value of test no 20                 :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 21                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 22                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 23                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    3.06
 p-value of test no 24                 :    0.03
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     932
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 29                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.61
 p-value of test no 32                 :    0.64
 
 Stat. AD after spacings (mNP2-S)      :    0.29
 p-value of test no 33                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    2.89
 p-value of test no 38                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 44                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 45                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.57
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.07
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.79
 p-value of test no 48                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.10
 p-value of test no 49                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.30
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 51                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.58
 p-value of test no 52                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.49
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.99
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.30
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1495.55
 p-value of test no 56                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7169.73
 p-value of test no 57                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 60                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.85
 p-value of test no 61                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.63
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.31
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  152.10
 p-value of test no 67                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4912.10
 p-value of test no 68                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45996
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869996
   j =  1                              :        399908009
   j =  2                              :            45994
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46384
 p-value of test no 71                 :  9.4e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870384
   j =  1                              :        399907233
   j =  2                              :            46382
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 74                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 76                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 79                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 81                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 94                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 97                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 102                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:36.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 104                :    0.95
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 105                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 107                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 110                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 3.75e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 114                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.91
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.98
 p-value of test no 117                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.50
 p-value of test no 118                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.75
 p-value of test no 119                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.18
 p-value of test no 120                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.92
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.84
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.41
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.10
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.62
 p-value of test no 125                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 128                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.97
 p-value of test no 129                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 131                :    0.15
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 132                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.72
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.32
 p-value of test no 134                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.69
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 136                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 137                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.55
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 140                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.85
 p-value of test no 141                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 144                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17265.21
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.82
 p-value of test no 146                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.16
 p-value of test no 147                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.32
 p-value of test no 148                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.20
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.63
 p-value of test no 150                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.33
 p-value of test no 151                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.42
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.65
 p-value of test no 153                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.13
 p-value of test no 154                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.34
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.59
 p-value of test no 157                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.95
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.72
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.80
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.67
 p-value of test no 161                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.26
 p-value of test no 162                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.88
 p-value of test no 163                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.19
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.82
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.54
 p-value of test no 166                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.65
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.11
 p-value of test no 168                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.66
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.13
 p-value of test no 170                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  442.14
 p-value of test no 171                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.63
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5094.01
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.20
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  250.79
 p-value of test no 175                :  8.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.07
 p-value of test no 176                :    0.70
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.56
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.52
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 179                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.74
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 183                :    0.71
 
 Sample variance                       :    2.34
 p-value of test no 184                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 187                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.098
 p-value of test no 188                :    0.54
 
 Sample variance                       :    1.12
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
 p-value of test no 191                :    0.77
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 192                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.45
 p-value of test no 196                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.29
 p-value of test no 198                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.79
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    2.22
 p-value of test no 206                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.20
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 210                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10008.20
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10142.00
 p-value of test no 215                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 216                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.049
 p-value of test no 218                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.32
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.53
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 224                :    0.01
 
 Anderson-Darling statistic = A2       :    2.65
 p-value of test no 225                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5037.30
 p-value of test no 226                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4021.05
 p-value of test no 227                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4080.98
 p-value of test no 228                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11938.73
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.77
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.40
 p-value of test no 231                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  8000121357
 
 Normal statistic for number of bits   :    0.96
 p-value of test no 232                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   60.78
 p-value of test no 233                :    0.25
 
 
 -----------------------------------------------
 Total number of bits:  7999958406
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.02
 p-value of test no 238                :    0.15
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.42
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.30
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.16
 p-value of test no 244                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.25
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.24
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.22
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 253                :    0.18
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:10.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35929
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 5                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 7                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 8                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 9                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 10                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 11                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5369
 p-value of test no 13                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7316
 p-value of test no 15                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4292
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4244
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7451
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.37
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 24                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 26                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    1.42
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.54
 p-value of test no 28                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 32                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 33                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.55
 p-value of test no 36                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     288
 p-value of test no 37                 :    0.74
 
 Stat. AD (mNP2)                       :    0.84
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 39                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.46
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 44                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 45                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.94
 p-value of test no 47                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.95
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.51
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.53
 p-value of test no 50                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.08
 p-value of test no 51                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.73
 p-value of test no 52                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.61
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.74
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  487.58
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1423.90
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6995.35
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.35
 p-value of test no 61                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.97
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.35
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  108.44
 p-value of test no 67                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4999.49
 p-value of test no 68                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45519
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869519
   j =  1                              :        399908966
   j =  2                              :            45511
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46041
 p-value of test no 71                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870041
   j =  1                              :        399907919
   j =  2                              :            46039
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 72                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 74                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 76                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 79                 :  7.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 81                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 85                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 88                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.11
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 95                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 101                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 106                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 110                :    0.44
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.88e-5
 p-value of test no 112                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 114                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 115                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 116                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.52
 p-value of test no 119                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.26
 p-value of test no 120                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   92.10
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.27
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.66
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.57
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.14
 p-value of test no 125                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 127                :  6.4e-3
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.44
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 130                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 131                :    0.88
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.12
 p-value of test no 133                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.09
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.16
 p-value of test no 135                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.30
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  121.26
 p-value of test no 141                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.12
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.54
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.83
 p-value of test no 146                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   52.63
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.58
 p-value of test no 148                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.64
 p-value of test no 149                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.86
 p-value of test no 150                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.18
 p-value of test no 151                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.28
 p-value of test no 152                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.94
 p-value of test no 153                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.96
 p-value of test no 154                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.31
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  180.43
 p-value of test no 156                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.89
 p-value of test no 157                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.79
 p-value of test no 158                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.08
 p-value of test no 159                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.00
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.40
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.04
 p-value of test no 162                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  521.02
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  120.82
 p-value of test no 164                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.45
 p-value of test no 165                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.59
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.33
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.25
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  423.83
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.31
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.61
 p-value of test no 171                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.42
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5042.65
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.45
 p-value of test no 174                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.36
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.52
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.51
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.68
 p-value of test no 179                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.70
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.85
 p-value of test no 184                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 186                :    0.80
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.98
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 192                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 195                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.63
 p-value of test no 196                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.70
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 202                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.79
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.45
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 208                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 209                :    0.19
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.64
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10036.92
 p-value of test no 215                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 216                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.038
 p-value of test no 217                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.36
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.29
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.84
 p-value of test no 226                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3942.06
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4155.77
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.88
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11809.61
 p-value of test no 230                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.86
 p-value of test no 231                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000082978
 
 Normal statistic for number of bits   :    0.66
 p-value of test no 232                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.27
 p-value of test no 233                :    0.43
 
 
 -----------------------------------------------
 Total number of bits:  8000076078
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 235                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 237                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.12
 p-value of test no 238                :    0.13
 
 Sample variance                       :    0.55
 p-value of test no 239                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.72
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 243                :    0.69
 
 Sample variance                       :    1.02
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 246                :    0.13
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.02
 p-value of test no 249                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
 p-value of test no 250                :    0.9961
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 251                :    0.02
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 252                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 253                :    0.01
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:29.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35930
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 7                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 11                 :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5475
 p-value of test no 13                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7251
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7408
 p-value of test no 18                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 19                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7416
 p-value of test no 20                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.54
 p-value of test no 22                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 24                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     880
 p-value of test no 25                 :    0.74
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.55
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     566
 p-value of test no 31                 :    0.92
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 32                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    3.28
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 34                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.36
 p-value of test no 35                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 38                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 40                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.53
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 45                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.14
 p-value of test no 46                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.12
 p-value of test no 47                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.28
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.56
 p-value of test no 49                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.95
 p-value of test no 50                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.11
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.41
 p-value of test no 52                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.58
 p-value of test no 53                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.71
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.06
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1432.83
 p-value of test no 56                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6885.22
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 58                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 59                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.11
 p-value of test no 61                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.48
 p-value of test no 65                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.54
 p-value of test no 66                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.87
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4906.37
 p-value of test no 68                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45460
 p-value of test no 70                 :    0.97
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869460
   j =  1                              :        399909081
   j =  2                              :            45458
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45403
 p-value of test no 71                 :    0.99
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869403
   j =  1                              :        399909196
   j =  2                              :            45399
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 77                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 79                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 81                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 84                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 90                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 93                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 95                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 97                 :  8.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    2.72
 p-value of test no 99                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.37
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-4
 p-value of test no 110                :    0.02
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
 p-value of test no 112                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
 p-value of test no 113                :    0.47
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.18
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 117                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.026
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.28
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.22
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.42
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.79
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.53
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.98
 p-value of test no 124                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.07
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 127                :    0.86
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.36
 p-value of test no 129                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 130                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.18
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.83
 p-value of test no 133                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.64
 p-value of test no 134                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    8.65
 p-value of test no 135                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 140                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.38
 p-value of test no 141                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    4.19
 p-value of test no 144                :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :16908.94
 p-value of test no 145                :    0.9976
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.68
 p-value of test no 146                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.98
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.10
 p-value of test no 148                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.03
 p-value of test no 149                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.20
 p-value of test no 150                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.03
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.83
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.30
 p-value of test no 153                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.64
 p-value of test no 154                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.58
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.11
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.99
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.46
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.02
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.39
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.66
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.87
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  566.11
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.85
 p-value of test no 164                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.79
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.93
 p-value of test no 166                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.23
 p-value of test no 167                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.82
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.52
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.75
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.42
 p-value of test no 171                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.02
 p-value of test no 172                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.86
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  356.75
 p-value of test no 174                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  221.06
 p-value of test no 175                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 176                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.26
 p-value of test no 177                :    0.99
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.50
 p-value of test no 178                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.49
 p-value of test no 179                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 182                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 188                :    0.36
 
 Sample variance                       :    0.38
 p-value of test no 189                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.43
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.82
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.32
 p-value of test no 198                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 200                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 202                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.84
 p-value of test no 203                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 204                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.44
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 209                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9941.14
 p-value of test no 211                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 212                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 213                :    0.12
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10241.81
 p-value of test no 215                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.26
 p-value of test no 216                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.69
 p-value of test no 218                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 219                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4953.53
 p-value of test no 222                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.22
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.50
 p-value of test no 226                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.70
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.97
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11764.25
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11714.28
 p-value of test no 230                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.39
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999888467
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.33
 p-value of test no 233                :    0.65
 
 
 -----------------------------------------------
 Total number of bits:  8000016558
 
 Normal statistic for number of bits   :    0.13
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 238                :    0.74
 
 Sample variance                       :    1.33
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.83
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.78
 p-value of test no 244                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 245                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 246                :    0.98
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 247                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.15
 p-value of test no 248                :    0.98
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 252                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 253                :    0.66
 
 Sample variance                       :    1.45
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.18
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:30.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35931
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 6                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 9                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 12                 :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5375
 p-value of test no 13                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 17                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 18                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 19                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7248
 p-value of test no 20                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 21                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 22                 :    0.44
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.16
 p-value of test no 23                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 26                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.51
 p-value of test no 30                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 32                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 33                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 34                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 38                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 40                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 41                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    2.14
 p-value of test no 42                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     185
 p-value of test no 43                 :  3.2e-3
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 45                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.27
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.03
 p-value of test no 47                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.72
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.74
 p-value of test no 49                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.85
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.62
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.84
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.91
 p-value of test no 53                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.76
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  418.11
 p-value of test no 55                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.26
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.05
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 60                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.24
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   80.00
 p-value of test no 65                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.99
 p-value of test no 66                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.81
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5020.32
 p-value of test no 68                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 70                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908279
   j =  2                              :            45853
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45641
 p-value of test no 71                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869641
   j =  1                              :        399908722
   j =  2                              :            45633
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 72                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 73                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 74                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 80                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 81                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 84                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 86                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 95                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 97                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 101                :    0.88
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 107                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
 p-value of test no 109                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 113                :    0.09
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 115                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 116                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.14
 p-value of test no 117                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 118                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.86
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.96
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.58
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.74
 p-value of test no 122                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.05
 p-value of test no 123                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.96
 p-value of test no 124                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.41
 p-value of test no 125                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.93
 p-value of test no 129                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 131                :    0.31
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.49
 p-value of test no 133                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.58
 p-value of test no 135                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 138                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.19
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 140                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.12
 p-value of test no 141                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 143                :    0.21
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17687.64
 p-value of test no 145                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.06
 p-value of test no 146                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.75
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.75
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.06
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.05
 p-value of test no 150                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   49.90
 p-value of test no 151                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.66
 p-value of test no 152                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.19
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.91
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.14
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.40
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.66
 p-value of test no 157                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.44
 p-value of test no 158                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.50
 p-value of test no 159                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.77
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.65
 p-value of test no 161                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.35
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  563.91
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.53
 p-value of test no 164                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.18
 p-value of test no 165                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.25
 p-value of test no 166                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.97
 p-value of test no 167                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.47
 p-value of test no 168                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.34
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.75
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.50
 p-value of test no 171                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.00
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4878.17
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.17
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.08
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.67
 p-value of test no 176                :    0.64
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.75
 p-value of test no 177                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   28.72
 p-value of test no 178                :  4.3e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.23
 p-value of test no 179                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 182                :    0.9967
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.87
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 188                :    0.34
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   38.00
 p-value of test no 197                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.43
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.72
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
 p-value of test no 205                :    0.9906
 
 Anderson-Darling statistic = A2       :    2.92
 p-value of test no 206                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  154.36
 p-value of test no 207                :    0.9928
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 210                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9891.72
 p-value of test no 211                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.32
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9984.76
 p-value of test no 215                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.75
 p-value of test no 216                :  3.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 221                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.19
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 224                :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 225                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.09
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.68
 p-value of test no 227                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.74
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12008.09
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11744.16
 p-value of test no 230                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.21
 p-value of test no 231                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000030379
 
 Normal statistic for number of bits   :    0.24
 p-value of test no 232                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.75
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  7999957716
 
 Normal statistic for number of bits   :   -0.33
 p-value of test no 234                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 236                :    0.23
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 237                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.27
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.39
 p-value of test no 239                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 240                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 241                :    0.11
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.58
 p-value of test no 244                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.69
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    1.87
 p-value of test no 249                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 250                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 251                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 252                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.84
 p-value of test no 253                :    0.03
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:27.76
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35932
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 4                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 5                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 6                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5397
 p-value of test no 13                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7304
 p-value of test no 15                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4264
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4275
 p-value of test no 17                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7287
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.00
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     881
 p-value of test no 25                 :    0.73
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.03
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 28                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.05
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 32                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 35                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    0.99
 p-value of test no 36                 :    0.36
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.56
 p-value of test no 38                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:18.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.52
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    1.27
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.62
 p-value of test no 46                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.33
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.96
 p-value of test no 48                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.89
 p-value of test no 49                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.76
 p-value of test no 51                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.54
 p-value of test no 52                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.38
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  195.15
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.25
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.89
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7019.29
 p-value of test no 57                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.49
 p-value of test no 61                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 64                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   74.24
 p-value of test no 65                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.34
 p-value of test no 66                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  133.61
 p-value of test no 67                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5211.29
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45969
 p-value of test no 70                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869969
   j =  1                              :        399908066
   j =  2                              :            45961
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45991
 p-value of test no 71                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869991
   j =  1                              :        399908021
   j =  2                              :            45985
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 72                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 77                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 87                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 91                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 92                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 93                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 95                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 98                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 103                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.20
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 105                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 107                :    0.62
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
 p-value of test no 109                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 110                :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 111                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
 p-value of test no 112                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 114                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 117                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.78
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.47
 p-value of test no 120                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   74.69
 p-value of test no 121                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.60
 p-value of test no 122                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.82
 p-value of test no 123                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.05
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.04
 p-value of test no 125                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 128                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.61
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 132                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.99
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 134                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.51
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 137                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.31
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 140                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.55
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 142                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17290.90
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.38
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.22
 p-value of test no 147                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :    8.57
 p-value of test no 148                :    0.9991    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.85
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.61
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.47
 p-value of test no 151                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.32
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.26
 p-value of test no 153                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.30
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.51
 p-value of test no 155                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.90
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.20
 p-value of test no 157                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.49
 p-value of test no 158                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.14
 p-value of test no 159                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.05
 p-value of test no 160                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.36
 p-value of test no 161                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.91
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.03
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.64
 p-value of test no 164                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.71
 p-value of test no 165                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.17
 p-value of test no 166                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.10
 p-value of test no 167                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4928.26
 p-value of test no 168                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.33
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.91
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.27
 p-value of test no 171                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  433.26
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.64
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.27
 p-value of test no 174                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.90
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.28
 p-value of test no 176                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.29
 p-value of test no 177                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.98
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.64
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    1.10
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 188                :    0.45
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 191                :    0.61
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 192                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
 p-value of test no 193                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 194                :    0.19
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 195                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.69
 p-value of test no 196                :    0.29
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.53
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 200                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  217.14
 p-value of test no 203                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 204                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 205                :    0.37
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 206                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.80
 p-value of test no 207                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 209                :    0.24
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.35
 p-value of test no 211                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.9903
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9983.34
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5008.28
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 224                :    0.99
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4736.59
 p-value of test no 226                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.78
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3930.41
 p-value of test no 228                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11721.75
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.83
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.88
 p-value of test no 231                :    0.89
 
 
 -----------------------------------------------
 Total number of bits:  7999866048
 
 Normal statistic for number of bits   :   -1.06
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.27
 p-value of test no 233                :    0.12
 
 
 -----------------------------------------------
 Total number of bits:  8000049351
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 236                :    0.36
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 237                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 238                :    0.27
 
 Sample variance                       :    0.91
 p-value of test no 239                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.45
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 242                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 245                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.60
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 247                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.75
 p-value of test no 248                :    0.77
 
 Sample variance                       :    1.43
 p-value of test no 249                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 251                :    0.78
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.95
 p-value of test no 253                :    0.83
 
 Sample variance                       :    0.92
 p-value of test no 254                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.54
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:06.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35933
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 4                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 10                 :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 11                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4355
 p-value of test no 14                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 15                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 16                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 18                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7516
 p-value of test no 19                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 20                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 22                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.18
 p-value of test no 23                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 24                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 26                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 27                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.18
 p-value of test no 30                 :    0.9955
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 32                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 34                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     300
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 39                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.92
 p-value of test no 44                 :    0.40
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 45                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.01
 p-value of test no 46                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.45
 p-value of test no 47                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.73
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.34
 p-value of test no 49                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.18
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.83
 p-value of test no 51                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.54
 p-value of test no 52                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.77
 p-value of test no 53                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.66
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.38
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1387.08
 p-value of test no 56                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6950.33
 p-value of test no 57                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 60                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.60
 p-value of test no 61                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 63                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 64                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.41
 p-value of test no 65                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.76
 p-value of test no 66                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  121.99
 p-value of test no 67                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.57
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45912
 p-value of test no 70                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869912
   j =  1                              :        399908180
   j =  2                              :            45904
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45751
 p-value of test no 71                 :    0.72
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869751
   j =  1                              :        399908503
   j =  2                              :            45741
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
 p-value of test no 72                 :    0.9987
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 74                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
 p-value of test no 79                 :    0.9957
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 84                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 85                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 92                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 99                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 101                :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 102                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.14
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.30
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
 p-value of test no 110                :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 111                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.45
 p-value of test no 115                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.08
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.60
 p-value of test no 117                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.17
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.13
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.79
 p-value of test no 120                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.72
 p-value of test no 121                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   20.96
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.65
 p-value of test no 123                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.55
 p-value of test no 124                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.47
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   26.86
 p-value of test no 129                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 132                :    0.9969
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.12
 p-value of test no 133                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.26
 p-value of test no 134                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.36
 p-value of test no 135                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 137                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 138                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.60
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 140                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  134.71
 p-value of test no 141                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 142                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17600.07
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.56
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.79
 p-value of test no 147                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.85
 p-value of test no 148                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.70
 p-value of test no 149                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.27
 p-value of test no 150                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.03
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.10
 p-value of test no 152                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.01
 p-value of test no 153                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.84
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.31
 p-value of test no 155                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.27
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.40
 p-value of test no 157                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.90
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.31
 p-value of test no 159                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.50
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.87
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  112.45
 p-value of test no 162                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.65
 p-value of test no 163                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.55
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.60
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.24
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.10
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.42
 p-value of test no 168                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  358.16
 p-value of test no 169                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.20
 p-value of test no 170                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.24
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.00
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5055.83
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.52
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.45
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.24
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.36
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.61
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.13
 p-value of test no 179                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 180                :  9.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 181                :    0.94
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.05
 p-value of test no 183                :    0.98
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 185                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.76
 
 Anderson-Darling statistic = A2       :    0.12
 p-value of test no 187                :    0.9998    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    1.13
 p-value of test no 189                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 190                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 192                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.17
 p-value of test no 198                :    0.11
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 202                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.48
 p-value of test no 203                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 204                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 206                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  232.04
 p-value of test no 207                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 208                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 209                :    0.93
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.90
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 213                :    0.86
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9804.17
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.35
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 218                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:03:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 221                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4922.54
 p-value of test no 222                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5061.67
 p-value of test no 226                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.57
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4084.22
 p-value of test no 228                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.03
 p-value of test no 229                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12124.60
 p-value of test no 230                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.46
 p-value of test no 231                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  8000074701
 
 Normal statistic for number of bits   :    0.59
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.58
 p-value of test no 233                :    0.75
 
 
 -----------------------------------------------
 Total number of bits:  7999898178
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 235                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.45
 p-value of test no 238                :    0.33
 
 Sample variance                       :    0.53
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.32
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 247                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.75
 p-value of test no 249                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 251                :    0.15
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 252                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.06
 p-value of test no 253                :    0.14
 
 Sample variance                       :    2.01
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:22.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35934
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 5                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 6                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 12                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5438
 p-value of test no 13                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4502
 p-value of test no 14                 :  6.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 15                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 18                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7438
 p-value of test no 19                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 20                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     904
 p-value of test no 25                 :    0.45
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 26                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     563
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    1.03
 p-value of test no 32                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.31
 p-value of test no 33                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.84
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 36                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    1.49
 p-value of test no 39                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.77
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.02
 p-value of test no 41                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    1.60
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     136
 p-value of test no 43                 :    0.87
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 44                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 45                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.59
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.81
 p-value of test no 47                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    6.36
 p-value of test no 48                 :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.10
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.56
 p-value of test no 50                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   72.49
 p-value of test no 51                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.36
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.46
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  279.74
 p-value of test no 54                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.47
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1503.98
 p-value of test no 56                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.54
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 58                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 60                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.66
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 62                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.54
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.69
 p-value of test no 66                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.42
 p-value of test no 67                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.94
 p-value of test no 68                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45982
 p-value of test no 70                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869982
   j =  1                              :        399908039
   j =  2                              :            45976
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45918
 p-value of test no 71                 :    0.43
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869918
   j =  1                              :        399908170
   j =  2                              :            45906
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 72                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 73                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 74                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 76                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 77                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 78                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 79                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 92                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 99                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.61
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 107                :    0.86
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 110                :    0.12
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 112                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.54
 p-value of test no 115                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.34
 p-value of test no 116                :  9.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 117                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.54
 p-value of test no 119                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.18
 p-value of test no 120                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.54
 p-value of test no 121                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.47
 p-value of test no 122                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.50
 p-value of test no 123                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.28
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.66
 p-value of test no 129                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 130                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.95
 p-value of test no 133                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.92
 p-value of test no 134                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 135                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.48
 p-value of test no 137                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 140                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  145.25
 p-value of test no 141                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 143                :    0.08
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 144                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17567.65
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   62.08
 p-value of test no 146                :  4.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.68
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.37
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.93
 p-value of test no 149                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.90
 p-value of test no 150                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.22
 p-value of test no 151                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.62
 p-value of test no 152                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.30
 p-value of test no 153                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.42
 p-value of test no 154                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.09
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.93
 p-value of test no 156                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.94
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  497.39
 p-value of test no 158                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.98
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.72
 p-value of test no 160                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  171.13
 p-value of test no 161                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.72
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  545.45
 p-value of test no 163                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.02
 p-value of test no 164                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.65
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.84
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.96
 p-value of test no 167                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.45
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.73
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.01
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.33
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.07
 p-value of test no 172                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4920.74
 p-value of test no 173                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.54
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.33
 p-value of test no 175                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.77
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 177                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.35
 p-value of test no 178                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 183                :    0.93
 
 Sample variance                       :    1.16
 p-value of test no 184                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 185                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 188                :    0.14
 
 Sample variance                       :    1.61
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
 p-value of test no 190                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
 p-value of test no 193                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.82
 p-value of test no 196                :    0.78
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.68
 p-value of test no 198                :    0.22
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 202                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  192.86
 p-value of test no 203                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.44
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.63
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.70
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 210                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9874.02
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.47
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9970.09
 p-value of test no 215                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.71
 p-value of test no 216                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 218                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 220                :    0.16
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 221                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4980.08
 p-value of test no 222                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4773.85
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4109.32
 p-value of test no 227                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4035.70
 p-value of test no 228                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11693.01
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11622.50
 p-value of test no 230                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.48
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  7999971558
 
 Normal statistic for number of bits   :   -0.22
 p-value of test no 232                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.45
 p-value of test no 233                :    0.09
 
 
 -----------------------------------------------
 Total number of bits:  8000089359
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 235                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.91
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.41
 p-value of test no 239                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 243                :    0.85
 
 Sample variance                       :    0.57
 p-value of test no 244                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 246                :    0.17
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 248                :    0.22
 
 Sample variance                       :    1.64
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 252                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 253                :    0.56
 
 Sample variance                       :    1.31
 p-value of test no 254                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:23.17
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35935
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 3                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 5                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 7                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 8                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 9                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 10                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 11                 :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 12                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5349
 p-value of test no 13                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7342
 p-value of test no 15                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 16                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4382
 p-value of test no 17                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7113
 p-value of test no 19                 :    0.9919
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 20                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 21                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 22                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    2.21
 p-value of test no 24                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     877
 p-value of test no 25                 :    0.77
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 30                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.29
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.44
 p-value of test no 34                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 38                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 40                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.67
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 45                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.94
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.58
 p-value of test no 47                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.61
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.92
 p-value of test no 49                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.41
 p-value of test no 50                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.13
 p-value of test no 51                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.91
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.37
 p-value of test no 53                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.31
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.34
 p-value of test no 55                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1371.85
 p-value of test no 56                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7212.33
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.44
 p-value of test no 59                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.77
 p-value of test no 61                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 62                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 64                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.35
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.22
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  140.02
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5140.45
 p-value of test no 68                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45616
 p-value of test no 70                 :    0.89
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869616
   j =  1                              :        399908773
   j =  2                              :            45606
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908027
   j =  2                              :            45982
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 73                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 74                 :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 77                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 79                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 83                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 88                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 94                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 95                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 99                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 100                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 101                :    0.02
 
 Anderson-Darling statistic = A2       :    2.64
 p-value of test no 102                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 103                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 104                :    0.99
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 108                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 8.35e-5
 p-value of test no 110                :    0.76
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 111                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.76e-4
 p-value of test no 112                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    3.38
 p-value of test no 114                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 116                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 118                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.73
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.99
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.88
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.68
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.80
 p-value of test no 124                :    0.9968
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.30
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 128                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.05
 p-value of test no 129                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 131                :    0.85
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 132                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.84
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.37
 p-value of test no 134                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.12
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.28
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.60
 p-value of test no 141                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17423.52
 p-value of test no 145                :    0.51
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.15
 p-value of test no 146                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.24
 p-value of test no 147                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.97
 p-value of test no 148                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.93
 p-value of test no 149                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.69
 p-value of test no 150                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.60
 p-value of test no 151                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.01
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.56
 p-value of test no 153                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.90
 p-value of test no 154                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.31
 p-value of test no 155                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.84
 p-value of test no 156                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.62
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  552.63
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.04
 p-value of test no 159                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.68
 p-value of test no 160                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.12
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.06
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.29
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.34
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.47
 p-value of test no 165                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.40
 p-value of test no 166                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.48
 p-value of test no 167                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.11
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.80
 p-value of test no 169                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.93
 p-value of test no 170                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.51
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.03
 p-value of test no 172                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4991.19
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  335.94
 p-value of test no 174                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.48
 p-value of test no 175                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.91
 p-value of test no 176                :    0.31
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.21
 p-value of test no 177                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.37
 p-value of test no 178                :    0.50
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 179                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 181                :    0.08
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.38
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 187                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 188                :    0.45
 
 Sample variance                       :    1.10
 p-value of test no 189                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
 p-value of test no 190                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
 p-value of test no 191                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 192                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 195                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.16
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.53
 p-value of test no 198                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 202                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.98
 p-value of test no 203                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 204                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
 p-value of test no 205                :    0.9931
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.69
 p-value of test no 207                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9876.53
 p-value of test no 211                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 214                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10066.69
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 217                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 218                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 219                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 220                :    0.21
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 221                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5006.32
 p-value of test no 222                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.38
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4063.64
 p-value of test no 227                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4283.40
 p-value of test no 228                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11783.58
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.15
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.79
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999988703
 
 Normal statistic for number of bits   :  -0.089
 p-value of test no 232                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.23
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999986726
 
 Normal statistic for number of bits   :   -0.10
 p-value of test no 234                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 237                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.71
 p-value of test no 238                :    0.04
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.13
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.83
 p-value of test no 243                :    0.97
 
 Sample variance                       :    1.04
 p-value of test no 244                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 246                :    0.12
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.55
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.21
 p-value of test no 249                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 250                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 251                :    0.89
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 252                :    0.9970
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 253                :    0.63
 
 Sample variance                       :    1.15
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:17.44
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35936
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 3                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 4                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 8                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1474
 p-value of test no 9                  :  1.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334594
   j =  1                              :        599997052
   j =  2                              :             1474
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 10                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 11                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5473
 p-value of test no 13                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 15                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4245
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7428
 p-value of test no 18                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 20                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 21                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.62
 p-value of test no 22                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 24                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.74
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.39
 p-value of test no 28                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 29                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    2.08
 p-value of test no 30                 :    0.08
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     634
 p-value of test no 31                 :    0.09
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.23
 p-value of test no 33                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.78
 p-value of test no 34                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 35                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.90
 p-value of test no 36                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    1.32
 p-value of test no 38                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 39                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 42                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    1.53
 p-value of test no 44                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    0.40
 p-value of test no 45                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.80
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.96
 p-value of test no 47                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.04
 p-value of test no 48                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.79
 p-value of test no 49                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.16
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.77
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.44
 p-value of test no 52                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   80.48
 p-value of test no 53                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  247.63
 p-value of test no 54                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.96
 p-value of test no 55                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1457.78
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7033.25
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.30
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 62                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 63                 :    0.03
 
 Anderson-Darling statistic = A2       :    4.36
 p-value of test no 64                 :  6.1e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :  100.47
 p-value of test no 65                 :  8.3e-4    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.51
 p-value of test no 66                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  109.72
 p-value of test no 67                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5065.42
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45854
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869854
   j =  1                              :        399908293
   j =  2                              :            45852
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907539
   j =  2                              :            46226
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 76                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 78                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 79                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 81                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 83                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 84                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 91                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 92                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
 p-value of test no 97                 :    0.9905
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 98                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.54
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 105                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
 p-value of test no 109                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 111                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
 p-value of test no 112                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 114                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.025
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 117                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 118                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.03
 p-value of test no 119                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.62
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.85
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.08
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.98
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.78
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.42
 p-value of test no 125                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 126                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 128                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.72
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 130                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 131                :    0.96
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.69
 p-value of test no 133                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.85
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.79
 p-value of test no 135                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.27
 p-value of test no 136                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 137                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.54
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 140                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.94
 p-value of test no 141                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 143                :    0.98
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 144                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17135.92
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.03
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.84
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.69
 p-value of test no 148                :    0.9944
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.95
 p-value of test no 149                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.01
 p-value of test no 150                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.01
 p-value of test no 151                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.80
 p-value of test no 152                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   33.32
 p-value of test no 153                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.99
 p-value of test no 154                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.91
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.58
 p-value of test no 156                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.68
 p-value of test no 157                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.94
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.38
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   55.26
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.43
 p-value of test no 161                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  168.83
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  492.85
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.43
 p-value of test no 164                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.57
 p-value of test no 165                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.76
 p-value of test no 166                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.57
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4926.30
 p-value of test no 168                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.74
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.56
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.37
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.06
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5141.52
 p-value of test no 173                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  400.96
 p-value of test no 174                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.18
 p-value of test no 175                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.35
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.63
 p-value of test no 177                :  4.3e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.88
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 180                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 181                :    0.21
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 187                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 188                :    0.43
 
 Sample variance                       :    1.36
 p-value of test no 189                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
 p-value of test no 191                :    0.47
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
 p-value of test no 193                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.92
 p-value of test no 196                :    0.66
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 198                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 200                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 201                :    0.03
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  228.19
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  220.17
 p-value of test no 207                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10027.89
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.40
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10032.45
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.52
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 217                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 218                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 220                :    0.94
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 221                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4813.03
 p-value of test no 222                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 224                :    0.90
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.09
 p-value of test no 226                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4125.14
 p-value of test no 227                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4173.29
 p-value of test no 228                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11729.40
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11811.05
 p-value of test no 230                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.46
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000003619
 
 Normal statistic for number of bits   :   0.029
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.23
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  7999943280
 
 Normal statistic for number of bits   :   -0.45
 p-value of test no 234                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 237                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.68
 p-value of test no 238                :    0.05
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 241                :    0.86
 
 Anderson-Darling statistic = A2       :    2.33
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.70
 p-value of test no 243                :    0.96
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.58
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.31
 p-value of test no 249                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 253                :    0.76
 
 Sample variance                       :    2.06
 p-value of test no 254                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:14.05
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  39  Run, r = 15                     8.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35937
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 3                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 7                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 8                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 11                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 12                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5384
 p-value of test no 13                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 14                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4420
 p-value of test no 16                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4408
 p-value of test no 17                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7265
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 24                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     895
 p-value of test no 25                 :    0.56
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.94
 p-value of test no 28                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.47
 p-value of test no 29                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 30                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    3.26
 p-value of test no 32                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 34                 :    0.80
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.74
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 39                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 40                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.24
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     167
 p-value of test no 43                 :    0.09
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 44                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.57
 p-value of test no 46                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.76
 p-value of test no 47                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.34
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.38
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.38
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.83
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.98
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.09
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.32
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  464.97
 p-value of test no 55                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1462.46
 p-value of test no 56                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7082.56
 p-value of test no 57                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   42.63
 p-value of test no 61                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 64                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.37
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.50
 p-value of test no 66                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.20
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.11
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908385
   j =  2                              :            45800
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45338
 p-value of test no 71                 :    0.9943
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869338
   j =  1                              :        399909326
   j =  2                              :            45334
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 74                 :    0.9971
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 79                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 81                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 85                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 88                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 91                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 92                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.47
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 99                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 101                :    0.91
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 102                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 104                :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 107                :    0.85
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-4
 p-value of test no 109                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    2.31
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
 p-value of test no 113                :    0.48
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 114                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 115                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.03
 p-value of test no 116                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.09
 p-value of test no 117                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.86
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.78
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.70
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   93.25
 p-value of test no 121                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.03
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.99
 p-value of test no 123                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   47.04
 p-value of test no 124                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   40.32
 p-value of test no 125                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 128                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   61.21
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 130                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 131                :    0.10
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 132                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.42
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.29
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.23
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.10
 p-value of test no 137                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 139                :  8.6e-3
 
 Anderson-Darling statistic = A2       :    3.79
 p-value of test no 140                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  169.81
 p-value of test no 141                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 144                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17238.36
 p-value of test no 145                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.24
 p-value of test no 146                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.28
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.04
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.38
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.77
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.57
 p-value of test no 151                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.81
 p-value of test no 152                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.36
 p-value of test no 153                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.28
 p-value of test no 154                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.82
 p-value of test no 155                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.47
 p-value of test no 156                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.06
 p-value of test no 157                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.92
 p-value of test no 158                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.95
 p-value of test no 159                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   99.03
 p-value of test no 160                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.00
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.23
 p-value of test no 162                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.20
 p-value of test no 163                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.05
 p-value of test no 164                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.34
 p-value of test no 165                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.27
 p-value of test no 166                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.69
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.59
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.05
 p-value of test no 169                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.78
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.81
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.03
 p-value of test no 172                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5017.21
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.35
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.29
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.50
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.33
 p-value of test no 177                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.45
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.45
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 182                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.027
 p-value of test no 183                :    0.49
 
 Sample variance                       :    1.56
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    1.17
 p-value of test no 189                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
 p-value of test no 193                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 195                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.36
 p-value of test no 196                :    0.14
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.75
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 201                :    0.08
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 202                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.40
 p-value of test no 203                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.06
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.57
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9955.44
 p-value of test no 211                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10030.31
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 219                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 221                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4821.41
 p-value of test no 222                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 225                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5015.60
 p-value of test no 226                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4004.08
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.35
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11795.87
 p-value of test no 229                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.81
 p-value of test no 230                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.33
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000039532
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 232                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.30
 p-value of test no 233                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  7999920831
 
 Normal statistic for number of bits   :   -0.63
 p-value of test no 234                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 237                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.061
 p-value of test no 238                :    0.52
 
 Sample variance                       :    0.94
 p-value of test no 239                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.65
 p-value of test no 244                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 247                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.62
 p-value of test no 248                :    0.05
 
 Sample variance                       :    2.33
 p-value of test no 249                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 250                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 252                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.76
 p-value of test no 254                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:21.79
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35938
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 3                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 4                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 5                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 8                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 9                  :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 10                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 11                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 12                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 14                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 16                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 17                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7312
 p-value of test no 18                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7333
 p-value of test no 19                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7425
 p-value of test no 20                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.99
 p-value of test no 22                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 24                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    2.11
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.00
 p-value of test no 27                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.07
 p-value of test no 29                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     637
 p-value of test no 31                 :    0.07
 
 Stat. AD (mNP2)                       :    3.08
 p-value of test no 32                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 34                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 35                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 36                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     303
 p-value of test no 37                 :    0.44
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 38                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.91
 p-value of test no 39                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 40                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.71
 p-value of test no 41                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.30
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 45                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.94
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.18
 p-value of test no 47                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.13
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.44
 p-value of test no 49                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.68
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.26
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.84
 p-value of test no 52                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.39
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  202.55
 p-value of test no 54                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.83
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.35
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7039.80
 p-value of test no 57                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.23
 p-value of test no 61                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 64                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.52
 p-value of test no 65                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    8.98
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.97
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5084.55
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45940
 p-value of test no 70                 :    0.39
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869940
   j =  1                              :        399908122
   j =  2                              :            45936
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46156
 p-value of test no 71                 :    0.10
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870156
   j =  1                              :        399907690
   j =  2                              :            46152
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 73                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 74                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 77                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 80                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 83                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 86                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 87                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 88                 :    0.9922
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.36
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 92                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
 p-value of test no 94                 :    0.9960
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 95                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9941
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.22
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 102                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 105                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 108                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
 p-value of test no 110                :    0.40
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 3.58e-5
 p-value of test no 113                :    0.95
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 114                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 115                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.20
 p-value of test no 116                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.012
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 118                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.89
 p-value of test no 119                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.53
 p-value of test no 120                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.10
 p-value of test no 121                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.55
 p-value of test no 122                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.36
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   53.14
 p-value of test no 124                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.69
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 127                :    0.96
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 128                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   27.70
 p-value of test no 129                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.26
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 132                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.88
 p-value of test no 133                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 134                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.35
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.04
 p-value of test no 137                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 138                :  2.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 139                :    0.96
 
 Anderson-Darling statistic = A2       :    5.77
 p-value of test no 140                :  1.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   86.91
 p-value of test no 141                :    0.9986
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.70
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17401.33
 p-value of test no 145                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.18
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.82
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.49
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.90
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.33
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.21
 p-value of test no 152                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.62
 p-value of test no 153                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.62
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.66
 p-value of test no 155                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.62
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.88
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.49
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.63
 p-value of test no 159                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.17
 p-value of test no 160                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.38
 p-value of test no 161                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.44
 p-value of test no 162                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  546.59
 p-value of test no 163                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.29
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.04
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.96
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.05
 p-value of test no 167                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4990.17
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  342.73
 p-value of test no 169                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.29
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.02
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.83
 p-value of test no 172                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5050.89
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.02
 p-value of test no 174                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.70
 p-value of test no 175                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.64
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.18
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.05
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.04
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.49
 p-value of test no 183                :    0.07
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 186                :    0.82
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 187                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.07
 p-value of test no 188                :    0.86
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.19
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 192                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
 p-value of test no 194                :    0.49
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 195                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.66
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.88
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.64
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.41
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.70
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.50
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 208                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10042.42
 p-value of test no 211                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 212                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 214                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10271.37
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.91
 p-value of test no 216                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.59
 p-value of test no 217                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.35
 p-value of test no 218                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 219                :    0.9901
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5087.36
 p-value of test no 222                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 223                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.72
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.45
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4203.72
 p-value of test no 227                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4095.43
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11829.62
 p-value of test no 229                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11945.35
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.43
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000004228
 
 Normal statistic for number of bits   :   0.033
 p-value of test no 232                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.46
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000076492
 
 Normal statistic for number of bits   :    0.60
 p-value of test no 234                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.67
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 237                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.29
 p-value of test no 238                :    0.39
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 242                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.00
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.63
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 248                :    0.71
 
 Sample variance                       :    1.55
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
 p-value of test no 250                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.05
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.47
 p-value of test no 253                :  6.7e-3
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:35:44.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           9.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35939
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9951
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 3                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1333
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334453
   j =  1                              :        599997334
   j =  2                              :             1333
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 6                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 9                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 11                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5583
 p-value of test no 13                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7376
 p-value of test no 15                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4287
 p-value of test no 16                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 17                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7297
 p-value of test no 18                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7388
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7221
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7198
 p-value of test no 21                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.33
 p-value of test no 23                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    0.32
 p-value of test no 24                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     892
 p-value of test no 25                 :    0.60
 
 Stat. AD (mNP2)                       :    1.13
 p-value of test no 26                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 28                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 30                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     654
 p-value of test no 31                 :    0.02
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 32                 :    0.96
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 33                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.34
 p-value of test no 40                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 41                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 42                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 44                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.02
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.25
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.13
 p-value of test no 47                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.50
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.25
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.00
 p-value of test no 51                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.66
 p-value of test no 52                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.95
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.69
 p-value of test no 54                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  411.91
 p-value of test no 55                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1415.54
 p-value of test no 56                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6898.16
 p-value of test no 57                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 60                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.58
 p-value of test no 61                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.87
 p-value of test no 65                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.86
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.53
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5206.76
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46073
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870073
   j =  1                              :        399907858
   j =  2                              :            46065
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45977
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869977
   j =  1                              :        399908049
   j =  2                              :            45971
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 74                 :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 76                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 78                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 81                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.01e+6
 p-value of test no 82                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 83                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 85                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:48.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 87                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 91                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 92                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 93                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 95                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 98                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 99                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 100                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 101                :    0.52
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 103                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
 p-value of test no 109                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 113                :    0.54
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 114                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.090
 p-value of test no 115                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 116                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.087
 p-value of test no 118                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   43.25
 p-value of test no 119                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.49
 p-value of test no 120                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.38
 p-value of test no 121                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.69
 p-value of test no 122                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.63
 p-value of test no 123                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.13
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.33
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 126                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.56
 p-value of test no 127                :  8.8e-4    *****
 
 Anderson-Darling statistic = A2       :    5.43
 p-value of test no 128                :  1.9e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   65.86
 p-value of test no 129                :  6.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.45
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.16
 p-value of test no 133                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.40
 p-value of test no 134                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.67
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   11.27
 p-value of test no 136                :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.19
 p-value of test no 137                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.90
 p-value of test no 141                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 142                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 144                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17448.69
 p-value of test no 145                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.63
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.98
 p-value of test no 147                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   54.32
 p-value of test no 148                :  6.0e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.83
 p-value of test no 149                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.88
 p-value of test no 150                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   47.19
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.78
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.38
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.42
 p-value of test no 154                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.78
 p-value of test no 155                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  183.92
 p-value of test no 156                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  100.85
 p-value of test no 157                :    0.9983
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  515.86
 p-value of test no 158                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.39
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.40
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.35
 p-value of test no 161                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.03
 p-value of test no 162                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.94
 p-value of test no 163                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.38
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.46
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  422.80
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.96
 p-value of test no 167                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5004.47
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.33
 p-value of test no 169                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.31
 p-value of test no 170                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.47
 p-value of test no 171                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.24
 p-value of test no 172                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4993.67
 p-value of test no 173                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  399.33
 p-value of test no 174                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.54
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.04
 p-value of test no 176                :    0.37
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 177                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.00
 p-value of test no 178                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.45
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 182                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.73
 p-value of test no 184                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 185                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.61
 p-value of test no 186                :  2.1e-4    *****
 
 Anderson-Darling statistic = A2       :    7.31
 p-value of test no 187                :  2.6e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.63
 p-value of test no 188                :  1.4e-4    *****
 
 Sample variance                       :    0.59
 p-value of test no 189                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 192                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.37
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 195                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.10
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 201                :    0.80
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 202                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.79
 p-value of test no 203                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 205                :    0.13
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.08
 p-value of test no 207                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 208                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.70
 p-value of test no 211                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 214                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9890.27
 p-value of test no 215                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.11
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.049
 p-value of test no 217                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.69
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.24
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 221                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.06
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 223                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 224                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4994.34
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3993.90
 p-value of test no 227                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4150.48
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12224.50
 p-value of test no 229                :  5.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11927.50
 p-value of test no 230                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.13
 p-value of test no 231                :    0.86
 
 
 -----------------------------------------------
 Total number of bits:  8000033982
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.22
 p-value of test no 233                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000003490
 
 Normal statistic for number of bits   :   0.028
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.32
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.17
 p-value of test no 238                :    0.12
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 240                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.70
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 242                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 243                :    0.76
 
 Sample variance                       :    1.40
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 245                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 246                :    0.05
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 248                :    0.17
 
 Sample variance                       :    0.83
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 250                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 252                :    0.46
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:36:15.28
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 J (L=50, r=0)       6.0e-4
  83  LempelZiv, r = 15               1.4e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35940
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 3                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 4                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1434
 p-value of test no 5                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334554
   j =  1                              :        599997132
   j =  2                              :             1434
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 6                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 8                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 9                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 10                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 12                 :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5436
 p-value of test no 13                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 16                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4232
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 18                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7387
 p-value of test no 19                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.56
 p-value of test no 22                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.38
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 26                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 27                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 29                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     645
 p-value of test no 31                 :    0.04
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 32                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 35                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.21
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 40                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 41                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 44                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.06
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.43
 p-value of test no 47                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.73
 p-value of test no 48                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.84
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.07
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.18
 p-value of test no 51                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.64
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.81
 p-value of test no 53                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  216.70
 p-value of test no 54                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  401.60
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1464.89
 p-value of test no 56                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7004.33
 p-value of test no 57                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 58                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   20.90
 p-value of test no 61                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.49
 p-value of test no 63                 :  5.2e-3
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   82.75
 p-value of test no 65                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.98
 p-value of test no 66                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.63
 p-value of test no 67                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4954.35
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9961
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907879
   j =  2                              :            46056
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45804
 p-value of test no 71                 :    0.64
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869804
   j =  1                              :        399908398
   j =  2                              :            45792
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 73                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 74                 :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 78                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.89
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 84                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 88                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 93                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 94                 :    0.89
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 95                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 99                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 100                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.39
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
 p-value of test no 107                :    0.9913
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
 p-value of test no 109                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
 p-value of test no 110                :    0.82
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 112                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 6.50e-5
 p-value of test no 113                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 115                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.83
 p-value of test no 116                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 117                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.25
 p-value of test no 118                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.31
 p-value of test no 119                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.52
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.96
 p-value of test no 121                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.59
 p-value of test no 122                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.70
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.12
 p-value of test no 124                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.78
 p-value of test no 125                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.66
 p-value of test no 129                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
 p-value of test no 130                :    0.9956
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.06
 
 Anderson-Darling statistic = A2       :    2.58
 p-value of test no 132                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   64.61
 p-value of test no 133                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.32
 p-value of test no 134                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.31
 p-value of test no 141                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 142                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 143                :    0.09
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 144                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17777.51
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.43
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.05
 p-value of test no 147                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.86
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.06
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.96
 p-value of test no 150                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.80
 p-value of test no 151                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.94
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.09
 p-value of test no 153                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.07
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.03
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.81
 p-value of test no 156                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.99
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  459.99
 p-value of test no 158                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.13
 p-value of test no 159                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.58
 p-value of test no 160                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.04
 p-value of test no 161                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.42
 p-value of test no 162                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.76
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.71
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.86
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.82
 p-value of test no 166                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.60
 p-value of test no 167                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4902.80
 p-value of test no 168                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.71
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.98
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.51
 p-value of test no 171                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.94
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4916.20
 p-value of test no 173                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.94
 p-value of test no 174                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.79
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.40
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.62
 p-value of test no 177                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.68
 p-value of test no 178                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.64
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 181                :    0.12
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 183                :    0.32
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 186                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.99
 p-value of test no 188                :    0.16
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
 p-value of test no 190                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 192                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 193                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
 p-value of test no 194                :    0.44
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 195                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.54
 p-value of test no 196                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.92
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.58
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 202                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.74
 p-value of test no 203                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 205                :    0.81
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.98
 p-value of test no 207                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 210                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10154.07
 p-value of test no 211                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 214                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9978.97
 p-value of test no 215                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 217                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 218                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 219                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.63
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4872.68
 p-value of test no 222                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 225                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.44
 p-value of test no 226                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.15
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4047.60
 p-value of test no 228                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11847.35
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11640.10
 p-value of test no 230                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.61
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000020740
 
 Normal statistic for number of bits   :    0.16
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.88
 p-value of test no 233                :    0.78
 
 
 -----------------------------------------------
 Total number of bits:  8000108079
 
 Normal statistic for number of bits   :    0.85
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 235                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 238                :    0.07
 
 Sample variance                       :    0.92
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 240                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 242                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.84
 p-value of test no 243                :    0.80
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 247                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.57
 p-value of test no 249                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 253                :    0.76
 
 Sample variance                       :    1.46
 p-value of test no 254                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:20.62
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35941
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1425
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334545
   j =  1                              :        599997150
   j =  2                              :             1425
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 9                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 10                 :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 12                 :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5501
 p-value of test no 13                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4407
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 15                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 16                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4418
 p-value of test no 17                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7470
 p-value of test no 18                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 19                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 20                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 23                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.71
 p-value of test no 24                 :    0.55
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 29                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     564
 p-value of test no 31                 :    0.93
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.73
 p-value of test no 34                 :    0.53
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 35                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.95
 p-value of test no 36                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     294
 p-value of test no 37                 :    0.62
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.82
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 40                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    1.25
 p-value of test no 42                 :    0.25
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     137
 p-value of test no 43                 :    0.85
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 44                 :    0.70
 
 Stat. AD after spacings (mNP2-S)      :    1.25
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.54
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 47                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.83
 p-value of test no 48                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.92
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.20
 p-value of test no 52                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.07
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  238.61
 p-value of test no 54                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.36
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1395.80
 p-value of test no 56                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.80
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.57
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.87
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 63                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 64                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.15
 p-value of test no 65                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.87
 p-value of test no 66                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.05
 p-value of test no 67                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5163.94
 p-value of test no 68                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45961
 p-value of test no 70                 :    0.35
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869961
   j =  1                              :        399908079
   j =  2                              :            45959
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45716
 p-value of test no 71                 :    0.78
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869716
   j =  1                              :        399908574
   j =  2                              :            45704
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 72                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 74                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 77                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 79                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 87                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.93
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 90                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 92                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 93                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.10
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 103                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 105                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 107                :    0.69
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 108                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
 p-value of test no 109                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.97e-5
 p-value of test no 112                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 113                :    0.30
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.067
 p-value of test no 115                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.27
 p-value of test no 116                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : -6.76e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.15
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.61
 p-value of test no 120                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.28
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   60.04
 p-value of test no 122                :  9.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.75
 p-value of test no 123                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.56
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.26
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 127                :    0.58
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.39
 p-value of test no 129                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 130                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 132                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   24.40
 p-value of test no 133                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.63
 p-value of test no 134                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.32
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.80
 p-value of test no 136                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 138                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.67
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.68
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.89
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.30
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.25
 p-value of test no 148                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.14
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.12
 p-value of test no 150                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.03
 p-value of test no 151                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.69
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   46.54
 p-value of test no 153                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.97
 p-value of test no 154                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.94
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.83
 p-value of test no 156                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.12
 p-value of test no 157                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  577.69
 p-value of test no 158                :  9.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.06
 p-value of test no 159                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.50
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 161                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.95
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.47
 p-value of test no 163                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  150.14
 p-value of test no 164                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.83
 p-value of test no 165                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.26
 p-value of test no 166                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.24
 p-value of test no 167                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.26
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  365.42
 p-value of test no 169                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  235.53
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.40
 p-value of test no 171                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.38
 p-value of test no 172                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.84
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  384.43
 p-value of test no 174                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  232.21
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.25
 p-value of test no 176                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.65
 p-value of test no 178                :    0.65
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.87
 p-value of test no 179                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 181                :    0.97
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.55
 p-value of test no 184                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.23
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.03
 p-value of test no 188                :    0.15
 
 Sample variance                       :    1.34
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
 p-value of test no 190                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
 p-value of test no 191                :    0.52
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
 p-value of test no 193                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 195                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   13.97
 p-value of test no 196                :    0.08
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.56
 p-value of test no 198                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 200                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 201                :    0.36
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.71
 p-value of test no 203                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 205                :    0.07
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 206                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  221.44
 p-value of test no 207                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 208                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 210                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10189.18
 p-value of test no 211                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.69
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 214                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9919.73
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.42
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 217                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 218                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 220                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 221                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.90
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 224                :    0.95
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 225                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4759.98
 p-value of test no 226                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4186.67
 p-value of test no 227                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.11
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11941.49
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11671.76
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.22
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000049210
 
 Normal statistic for number of bits   :    0.39
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.28
 p-value of test no 233                :    0.54
 
 
 -----------------------------------------------
 Total number of bits:  8000005671
 
 Normal statistic for number of bits   :   0.045
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 236                :    0.28
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 237                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 238                :    0.67
 
 Sample variance                       :    0.23
 p-value of test no 239                :    0.9903
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 248                :    0.45
 
 Sample variance                       :    1.73
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 253                :    0.66
 
 Sample variance                       :    0.61
 p-value of test no 254                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:51.57
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35942
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 3                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 5                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 6                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 7                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 8                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 9                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 10                 :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1456
 p-value of test no 12                 :  7.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334576
   j =  1                              :        599997088
   j =  2                              :             1456
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4320
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 15                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 16                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7336
 p-value of test no 18                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7295
 p-value of test no 19                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 20                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 21                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 24                 :    0.45
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 27                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 28                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 29                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.18
 p-value of test no 34                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 35                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.36
 p-value of test no 36                 :    0.89
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     301
 p-value of test no 37                 :    0.48
 
 Stat. AD (mNP2)                       :    0.72
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 40                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.84
 p-value of test no 41                 :    0.45
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 42                 :    0.92
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 45                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 46                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.00
 p-value of test no 47                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.60
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.95
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.65
 p-value of test no 50                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.39
 p-value of test no 51                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.03
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   71.23
 p-value of test no 53                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.80
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  429.35
 p-value of test no 55                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:16.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.38
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6909.69
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.91
 p-value of test no 61                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 64                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   46.64
 p-value of test no 65                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.25
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  115.48
 p-value of test no 67                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4929.85
 p-value of test no 68                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46425
 p-value of test no 70                 :  5.5e-3
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870425
   j =  1                              :        399907154
   j =  2                              :            46417
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45891
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869891
   j =  1                              :        399908221
   j =  2                              :            45885
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 72                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 76                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 78                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 79                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
 p-value of test no 80                 :    0.9973
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 85                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 90                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 95                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.52
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 99                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 102                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 104                :    0.91
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 106                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 108                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 109                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
 p-value of test no 110                :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.17e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
 p-value of test no 113                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 115                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.72
 p-value of test no 116                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.51
 p-value of test no 117                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.77
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.71
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   48.09
 p-value of test no 120                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.38
 p-value of test no 121                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.17
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.66
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 124                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.94
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.64
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 128                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.06
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 131                :    0.86
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.94
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.55
 p-value of test no 134                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.49
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 137                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 139                :    0.91
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.04
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 144                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17585.36
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.93
 p-value of test no 147                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.54
 p-value of test no 148                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.96
 p-value of test no 149                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.10
 p-value of test no 150                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.48
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.73
 p-value of test no 152                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.41
 p-value of test no 153                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.21
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.86
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.65
 p-value of test no 156                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.83
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  501.49
 p-value of test no 158                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  161.45
 p-value of test no 159                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.23
 p-value of test no 160                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.29
 p-value of test no 161                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.06
 p-value of test no 162                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  525.54
 p-value of test no 163                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.96
 p-value of test no 164                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.68
 p-value of test no 165                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.84
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  397.48
 p-value of test no 167                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5009.52
 p-value of test no 168                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.42
 p-value of test no 169                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.53
 p-value of test no 170                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.16
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.65
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4983.58
 p-value of test no 173                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.17
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.86
 p-value of test no 175                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    5.74
 p-value of test no 176                :    0.93
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   19.79
 p-value of test no 178                :    0.07
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 179                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.94
 p-value of test no 184                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.21
 p-value of test no 188                :    0.58
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 192                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 194                :    0.80
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 195                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.46
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.66
 p-value of test no 198                :    0.95
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.27
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.23
 p-value of test no 203                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.33
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 206                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.15
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.39
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.78
 p-value of test no 211                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9907.43
 p-value of test no 215                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.94
 p-value of test no 217                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 221                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4902.76
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 223                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 225                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5046.94
 p-value of test no 226                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4311.79
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.74
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11705.09
 p-value of test no 229                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11709.21
 p-value of test no 230                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.88
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999888092
 
 Normal statistic for number of bits   :   -0.88
 p-value of test no 232                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.47
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999899345
 
 Normal statistic for number of bits   :   -0.80
 p-value of test no 234                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.48
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 238                :    0.22
 
 Sample variance                       :    1.46
 p-value of test no 239                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 242                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 243                :    0.66
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 247                :    0.81
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.041
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.33
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 252                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.035
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.29
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:45:27.81
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35943
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 3                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 4                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 6                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 9                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 10                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 11                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 12                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5463
 p-value of test no 13                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7299
 p-value of test no 15                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4397
 p-value of test no 16                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4364
 p-value of test no 17                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7224
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7324
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.51
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.53
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 24                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     905
 p-value of test no 25                 :    0.44
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 26                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 27                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.72
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 29                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 30                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     592
 p-value of test no 31                 :    0.62
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 36                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     266
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.46
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.37
 p-value of test no 41                 :    0.88
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 42                 :    0.19
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    2.44
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 45                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.70
 p-value of test no 46                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.45
 p-value of test no 47                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.18
 p-value of test no 48                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    7.73
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.80
 p-value of test no 50                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.95
 p-value of test no 51                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.96
 p-value of test no 52                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.16
 p-value of test no 53                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.68
 p-value of test no 54                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.54
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1404.33
 p-value of test no 56                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6919.73
 p-value of test no 57                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 60                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.59
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.23
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.63
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.27
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5048.75
 p-value of test no 68                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9909
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 70                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908144
   j =  2                              :            45919
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45951
 p-value of test no 71                 :    0.37
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869951
   j =  1                              :        399908103
   j =  2                              :            45941
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 72                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 74                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.49
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 76                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 77                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 78                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 80                 :    0.67
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 85                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 87                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 91                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 92                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 95                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.96
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 99                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 100                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 103                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 106                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
 p-value of test no 110                :    0.72
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 111                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 114                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.095
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 116                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 118                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.88
 p-value of test no 119                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.71
 p-value of test no 120                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.87
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.05
 p-value of test no 122                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.09
 p-value of test no 123                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.63
 p-value of test no 124                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.02
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.63
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.80
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.28
 p-value of test no 134                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.54
 p-value of test no 135                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 136                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 137                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 140                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  110.69
 p-value of test no 141                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 144                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17382.80
 p-value of test no 145                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.05
 p-value of test no 146                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.79
 p-value of test no 147                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.90
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.50
 p-value of test no 149                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.69
 p-value of test no 150                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.06
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.35
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.18
 p-value of test no 153                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.25
 p-value of test no 154                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.11
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.14
 p-value of test no 156                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.85
 p-value of test no 157                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.99
 p-value of test no 158                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.33
 p-value of test no 159                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.25
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.06
 p-value of test no 161                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.45
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  415.98
 p-value of test no 163                :    0.9975
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  106.61
 p-value of test no 164                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   66.72
 p-value of test no 165                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.39
 p-value of test no 166                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.09
 p-value of test no 167                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4980.73
 p-value of test no 168                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.31
 p-value of test no 169                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  173.88
 p-value of test no 170                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.13
 p-value of test no 171                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  437.17
 p-value of test no 172                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4982.55
 p-value of test no 173                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  412.59
 p-value of test no 174                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.47
 p-value of test no 175                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.93
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.82
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.98
 p-value of test no 179                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 181                :    0.89
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 182                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 183                :    0.79
 
 Sample variance                       :    1.55
 p-value of test no 184                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.52
 p-value of test no 185                :  2.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    5.61
 p-value of test no 187                :  1.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.11
 p-value of test no 188                :    0.9991    *****
 
 Sample variance                       :    0.52
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
 p-value of test no 191                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.14
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.94
 p-value of test no 198                :    0.94
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.29
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.78
 p-value of test no 203                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 205                :    0.87
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.37
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 209                :    0.44
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 210                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.32
 p-value of test no 211                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 212                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.34
 p-value of test no 215                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.98
 p-value of test no 217                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.81
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 223                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.50
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 225                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4946.15
 p-value of test no 226                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4177.09
 p-value of test no 227                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4087.50
 p-value of test no 228                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11786.54
 p-value of test no 229                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.41
 p-value of test no 230                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.35
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  8000021517
 
 Normal statistic for number of bits   :    0.17
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.73
 p-value of test no 233                :    0.56
 
 
 -----------------------------------------------
 Total number of bits:  8000001126
 
 Normal statistic for number of bits   : 8.90e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 235                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 237                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.88
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.07
 p-value of test no 239                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 240                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.20
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 242                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 243                :    0.21
 
 Sample variance                       :    0.48
 p-value of test no 244                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.43
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.63
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.11
 p-value of test no 249                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 253                :    0.69
 
 Sample variance                       :    0.27
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.62
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:32.82
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35944
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1415
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334535
   j =  1                              :        599997170
   j =  2                              :             1415
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 4                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 5                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 7                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 9                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 10                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 11                 :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 12                 :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5400
 p-value of test no 13                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7488
 p-value of test no 15                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4415
 p-value of test no 16                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4322
 p-value of test no 17                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 19                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7283
 p-value of test no 20                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7468
 p-value of test no 21                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 22                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.45
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     922
 p-value of test no 25                 :    0.24
 
 Stat. AD (mNP2)                       :    1.18
 p-value of test no 26                 :    0.27
 
 Stat. AD after spacings (mNP2-S)      :    2.06
 p-value of test no 27                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.90
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 32                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.08
 p-value of test no 33                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.27
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.70
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     304
 p-value of test no 37                 :    0.42
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 41                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 42                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.26
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.49
 p-value of test no 46                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.82
 p-value of test no 47                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.71
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.62
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.71
 p-value of test no 50                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 51                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.46
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.65
 p-value of test no 53                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  193.07
 p-value of test no 54                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.15
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1491.70
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7005.06
 p-value of test no 57                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 58                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.06
 p-value of test no 61                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 64                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   40.55
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.13
 p-value of test no 66                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.55
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5088.68
 p-value of test no 68                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908116
   j =  2                              :            45939
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45574
 p-value of test no 71                 :    0.92
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869574
   j =  1                              :        399908856
   j =  2                              :            45566
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 78                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 81                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 83                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 84                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 92                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    4.17
 p-value of test no 95                 :  7.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 1.99e+6
 p-value of test no 96                 :    0.9974
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 99                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.47
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 105                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 108                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
 p-value of test no 110                :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 111                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
 p-value of test no 112                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
 p-value of test no 113                :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 114                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.024
 p-value of test no 115                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.94
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.05
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.94
 p-value of test no 120                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.30
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.00
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   50.72
 p-value of test no 123                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.05
 p-value of test no 124                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.62
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 126                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.55
 p-value of test no 129                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 130                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.64
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 132                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.22
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.38
 p-value of test no 134                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.26
 p-value of test no 135                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 136                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 139                :    0.86
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  111.94
 p-value of test no 141                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 144                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17569.71
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.47
 p-value of test no 146                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.06
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.13
 p-value of test no 148                :    0.9963
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.03
 p-value of test no 149                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.40
 p-value of test no 150                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.35
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.10
 p-value of test no 152                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.08
 p-value of test no 153                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.53
 p-value of test no 154                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.47
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.89
 p-value of test no 156                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.49
 p-value of test no 157                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.14
 p-value of test no 158                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.01
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.04
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.98
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.76
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  526.21
 p-value of test no 163                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.60
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.42
 p-value of test no 165                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  402.76
 p-value of test no 166                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.83
 p-value of test no 167                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4886.67
 p-value of test no 168                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.60
 p-value of test no 169                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.54
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  456.33
 p-value of test no 171                :  6.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  339.24
 p-value of test no 172                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4992.21
 p-value of test no 173                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  407.95
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.04
 p-value of test no 175                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.21
 p-value of test no 176                :    0.14
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 177                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.34
 p-value of test no 179                :    0.63
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 182                :    0.80
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.34
 p-value of test no 183                :    0.63
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 185                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.56
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.79
 p-value of test no 188                :    0.78
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
 p-value of test no 190                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
 p-value of test no 194                :    0.79
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 195                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.05
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.61
 p-value of test no 198                :    0.58
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 201                :    0.52
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 202                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.25
 p-value of test no 203                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.20
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.29
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10011.07
 p-value of test no 211                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 213                :    0.08
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10152.43
 p-value of test no 215                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 216                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.30
 p-value of test no 217                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.60
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4915.94
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 225                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.26
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4243.08
 p-value of test no 227                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.67
 p-value of test no 228                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11771.24
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11778.11
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.36
 p-value of test no 231                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  7999929318
 
 Normal statistic for number of bits   :   -0.56
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.02
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000108625
 
 Normal statistic for number of bits   :    0.86
 p-value of test no 234                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 235                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.68
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 237                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 238                :    0.72
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 241                :    0.24
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.36
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.88
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 248                :    0.59
 
 Sample variance                       :    0.78
 p-value of test no 249                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 250                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 251                :    0.06
 
 Anderson-Darling statistic = A2       :    3.70
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 253                :    0.01
 
 Sample variance                       :    2.63
 p-value of test no 254                :  4.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.69
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:56.98
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35945
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 5                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1436
 p-value of test no 6                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334556
   j =  1                              :        599997128
   j =  2                              :             1436
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 7                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 8                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1503
 p-value of test no 9                  :  1.1e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334623
   j =  1                              :        599996994
   j =  2                              :             1503
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1306
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334426
   j =  1                              :        599997388
   j =  2                              :             1306
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 11                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4389
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7127
 p-value of test no 15                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4283
 p-value of test no 16                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 17                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7155
 p-value of test no 18                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7204
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 21                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.77
 p-value of test no 23                 :    0.50
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 27                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 28                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.35
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     545
 p-value of test no 31                 :    0.99
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 32                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 33                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.49
 p-value of test no 34                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.85
 p-value of test no 35                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     265
 p-value of test no 37                 :    0.98
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.86
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 39                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 40                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 41                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 42                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 44                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.16
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.01
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.09
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.61
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.14
 p-value of test no 50                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.31
 p-value of test no 51                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.86
 p-value of test no 52                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.03
 p-value of test no 53                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.06
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.04
 p-value of test no 55                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1475.20
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6982.98
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 58                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 60                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.00
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 62                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 63                 :    0.91
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 64                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   42.83
 p-value of test no 65                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.90
 p-value of test no 66                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.19
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.18
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45608
 p-value of test no 70                 :    0.90
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869608
   j =  1                              :        399908789
   j =  2                              :            45598
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45671
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869671
   j =  1                              :        399908662
   j =  2                              :            45663
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 74                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.78
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 77                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 81                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 84                 :  4.9e-3
 
 Anderson-Darling statistic = A2       :    2.75
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 88                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 90                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 92                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 94                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 97                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 99                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 106                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 108                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
 p-value of test no 109                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
 p-value of test no 110                :    0.34
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
 p-value of test no 112                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 115                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.76
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.17
 p-value of test no 119                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.33
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.12
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.08
 p-value of test no 122                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   64.02
 p-value of test no 123                :  3.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.65
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.30
 p-value of test no 125                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 126                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 127                :    0.05
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 128                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.32
 p-value of test no 129                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 131                :    0.79
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 132                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.69
 p-value of test no 133                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.56
 p-value of test no 134                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.72
 p-value of test no 135                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 136                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 138                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 139                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  112.96
 p-value of test no 141                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 142                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 143                :    0.77
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 144                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17392.67
 p-value of test no 145                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.19
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.39
 p-value of test no 147                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.43
 p-value of test no 148                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.15
 p-value of test no 149                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.92
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.46
 p-value of test no 152                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.47
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.20
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.96
 p-value of test no 155                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.36
 p-value of test no 156                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.49
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  523.19
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.51
 p-value of test no 159                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.57
 p-value of test no 160                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.77
 p-value of test no 161                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.28
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  538.42
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.39
 p-value of test no 164                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.80
 p-value of test no 165                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.43
 p-value of test no 166                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.23
 p-value of test no 167                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4895.11
 p-value of test no 168                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.28
 p-value of test no 169                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.98
 p-value of test no 170                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  386.24
 p-value of test no 171                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  440.62
 p-value of test no 172                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5158.72
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.18
 p-value of test no 174                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  183.17
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.53
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.84
 p-value of test no 177                :    0.80
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.28
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.54
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 182                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 185                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.03
 p-value of test no 189                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 195                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.42
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.00
 p-value of test no 198                :    0.65
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 201                :    0.77
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 202                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.64
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.72
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 206                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.15
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.09
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10181.78
 p-value of test no 211                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.74
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.69
 p-value of test no 216                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 217                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 218                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 221                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4937.09
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 224                :    0.11
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.89
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4058.56
 p-value of test no 227                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4246.11
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12020.62
 p-value of test no 229                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11816.91
 p-value of test no 230                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.15
 p-value of test no 231                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999871697
 
 Normal statistic for number of bits   :   -1.01
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.11
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000046726
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 235                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 236                :    0.33
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 237                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 238                :    0.58
 
 Sample variance                       :    1.54
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 240                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 242                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 243                :    0.83
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.62
 
 Sample variance                       :    1.16
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 252                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 253                :    0.57
 
 Sample variance                       :    0.82
 p-value of test no 254                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:44.39
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           1.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35946
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 3                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 4                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1271
 p-value of test no 5                  :    0.9944
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334391
   j =  1                              :        599997458
   j =  2                              :             1271
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 6                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 7                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 8                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 10                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 11                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 12                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4323
 p-value of test no 14                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7227
 p-value of test no 15                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4309
 p-value of test no 16                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4344
 p-value of test no 17                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 19                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 23                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.75
 p-value of test no 24                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     842
 p-value of test no 25                 :    0.97
 
 Stat. AD (mNP2)                       :    0.89
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 27                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.05
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 29                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    2.43
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 33                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.57
 
 Test on the Nm values of W_{n,i}(mNP1):    2.51
 p-value of test no 36                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.90
 p-value of test no 40                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 42                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 44                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    1.59
 p-value of test no 45                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.77
 p-value of test no 46                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.58
 p-value of test no 47                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.18
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   29.12
 p-value of test no 49                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.68
 p-value of test no 50                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.16
 p-value of test no 51                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.94
 p-value of test no 52                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   73.80
 p-value of test no 53                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  272.70
 p-value of test no 54                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.83
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.28
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7111.74
 p-value of test no 57                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 60                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.68
 p-value of test no 61                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 62                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 63                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 64                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.58
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.87
 p-value of test no 66                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  101.42
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5035.07
 p-value of test no 68                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45692
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869692
   j =  1                              :        399908618
   j =  2                              :            45688
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45892
 p-value of test no 71                 :    0.48
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869892
   j =  1                              :        399908219
   j =  2                              :            45886
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 72                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 74                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 76                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 77                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 78                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 79                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 81                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 83                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 88                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 91                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 92                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 102                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 105                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.57e-6
 p-value of test no 109                :    0.9971
 
 Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
 p-value of test no 110                :    0.06
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 111                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
 p-value of test no 112                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 114                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 115                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.057
 p-value of test no 116                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 117                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.12
 p-value of test no 118                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.16
 p-value of test no 119                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.05
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.15
 p-value of test no 121                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.23
 p-value of test no 122                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.24
 p-value of test no 123                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.49
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   18.52
 p-value of test no 125                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 126                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.20
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.59
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 130                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.05
 p-value of test no 133                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.83
 p-value of test no 134                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.87
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 140                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  142.54
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 142                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 144                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17743.00
 p-value of test no 145                :    0.05
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   53.88
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.87
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.39
 p-value of test no 148                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.47
 p-value of test no 149                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.70
 p-value of test no 150                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.61
 p-value of test no 151                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.00
 p-value of test no 152                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   39.66
 p-value of test no 153                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.56
 p-value of test no 154                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.72
 p-value of test no 155                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.45
 p-value of test no 156                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.00
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.12
 p-value of test no 158                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.65
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   89.50
 p-value of test no 160                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  185.53
 p-value of test no 161                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.79
 p-value of test no 162                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.73
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.90
 p-value of test no 164                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.27
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.95
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.48
 p-value of test no 167                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.05
 p-value of test no 168                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.39
 p-value of test no 169                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  181.33
 p-value of test no 170                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.16
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.05
 p-value of test no 172                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5051.38
 p-value of test no 173                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.37
 p-value of test no 174                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.86
 p-value of test no 175                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.09
 p-value of test no 176                :    0.24
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.70
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.87
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.87
 p-value of test no 179                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 182                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 183                :    0.48
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 185                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 187                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 188                :    0.88
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
 p-value of test no 190                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 191                :    0.16
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.86
 p-value of test no 196                :    0.35
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.90
 p-value of test no 198                :    0.87
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 202                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.66
 p-value of test no 203                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.27
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 206                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.18
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 210                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10051.16
 p-value of test no 211                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 214                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.36
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 216                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 217                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.45
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.24
 p-value of test no 222                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.55
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 225                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.77
 p-value of test no 226                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.65
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.91
 p-value of test no 228                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11765.82
 p-value of test no 229                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11507.29
 p-value of test no 230                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.46
 p-value of test no 231                :    0.10
 
 
 -----------------------------------------------
 Total number of bits:  8000198550
 
 Normal statistic for number of bits   :    1.57
 p-value of test no 232                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.23
 p-value of test no 233                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000045088
 
 Normal statistic for number of bits   :    0.36
 p-value of test no 234                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 236                :    0.19
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 237                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 238                :    0.14
 
 Sample variance                       :    0.87
 p-value of test no 239                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 242                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.75
 p-value of test no 243                :    0.23
 
 Sample variance                       :    1.15
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.21
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 251                :    0.81
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 252                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 253                :    0.84
 
 Sample variance                       :    0.60
 p-value of test no 254                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:11.59
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35947
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 3                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 4                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1458
 p-value of test no 5                  :  6.2e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334578
   j =  1                              :        599997084
   j =  2                              :             1458
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1266
 p-value of test no 6                  :    0.9963
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334386
   j =  1                              :        599997468
   j =  2                              :             1266
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1435
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334555
   j =  1                              :        599997130
   j =  2                              :             1435
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 8                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 9                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 10                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 11                 :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 12                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5409
 p-value of test no 13                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 14                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4265
 p-value of test no 16                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4435
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7535
 p-value of test no 19                 :  5.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 20                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 21                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 22                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.64
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.97
 p-value of test no 24                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     851
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    3.77
 p-value of test no 26                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.14
 p-value of test no 27                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.89
 p-value of test no 28                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.76
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 30                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.69
 p-value of test no 34                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 35                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     289
 p-value of test no 37                 :    0.73
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 38                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    0.55
 p-value of test no 39                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 40                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 41                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 42                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    1.08
 p-value of test no 44                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 45                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.07
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.37
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.35
 p-value of test no 48                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.75
 p-value of test no 49                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.88
 p-value of test no 50                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.41
 p-value of test no 51                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.32
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.86
 p-value of test no 53                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.48
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.97
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1486.83
 p-value of test no 56                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.62
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.54
 p-value of test no 58                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.59
 
 Anderson-Darling statistic = A2       :    2.40
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.61
 p-value of test no 61                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 63                 :    0.99
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 64                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   45.85
 p-value of test no 65                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.12
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.59
 p-value of test no 67                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5085.96
 p-value of test no 68                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45235
 p-value of test no 70                 :    0.9987
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869235
   j =  1                              :        399909533
   j =  2                              :            45229
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45625
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869625
   j =  1                              :        399908751
   j =  2                              :            45623
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 73                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 74                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 77                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 78                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.12
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 85                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 86                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    3.34
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 91                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 92                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 94                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 95                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
 p-value of test no 98                 :    0.9905
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 99                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 101                :    0.46
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 102                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 105                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.37
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
 p-value of test no 109                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.30e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 114                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.69
 p-value of test no 115                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 117                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.54
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.81
 p-value of test no 120                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.12
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.21
 p-value of test no 122                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.75
 p-value of test no 124                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.36
 p-value of test no 125                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.08
 
 Anderson-Darling statistic = A2       :    1.88
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.62
 p-value of test no 129                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
 p-value of test no 130                :    0.9913
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 131                :    0.19
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 132                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   57.19
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.47
 p-value of test no 134                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.40
 p-value of test no 135                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.49
 p-value of test no 136                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 137                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 140                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.98
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 142                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 144                :    0.9953
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17465.02
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.97
 p-value of test no 146                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.22
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   38.13
 p-value of test no 148                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.61
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.53
 p-value of test no 150                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.08
 p-value of test no 151                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   16.94
 p-value of test no 152                :    0.9957
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.87
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.01
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.12
 p-value of test no 155                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.95
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.69
 p-value of test no 157                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.32
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  121.30
 p-value of test no 159                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.97
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.39
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.95
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.38
 p-value of test no 163                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  152.93
 p-value of test no 164                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.36
 p-value of test no 165                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  356.71
 p-value of test no 166                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.32
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5075.69
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  382.02
 p-value of test no 169                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.61
 p-value of test no 170                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.39
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.11
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.15
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  366.37
 p-value of test no 174                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.19
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.61
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.72
 p-value of test no 178                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.26
 p-value of test no 179                :    0.10
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 182                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 183                :    0.57
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 187                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.49
 p-value of test no 189                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
 p-value of test no 190                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.34
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.57
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   15.07
 p-value of test no 198                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 200                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.19
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 202                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  223.16
 p-value of test no 203                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 204                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.24
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 206                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.98
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9698.58
 p-value of test no 211                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.48
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9885.75
 p-value of test no 215                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 216                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.49
 p-value of test no 217                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 218                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4825.13
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 224                :    0.05
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 225                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4988.59
 p-value of test no 226                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.89
 p-value of test no 227                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4097.24
 p-value of test no 228                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11879.17
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.77
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.97
 p-value of test no 231                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999919532
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.53
 p-value of test no 233                :    0.61
 
 
 -----------------------------------------------
 Total number of bits:  8000101107
 
 Normal statistic for number of bits   :    0.80
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.55
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    1.96
 p-value of test no 239                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 241                :    0.73
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.24
 p-value of test no 243                :    0.89
 
 Sample variance                       :    0.51
 p-value of test no 244                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.68
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 247                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.80
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 252                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.41
 p-value of test no 254                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:43.36
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35948
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 3                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 4                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 5                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 6                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 7                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 8                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 10                 :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5334
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7163
 p-value of test no 15                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4302
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4348
 p-value of test no 17                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 19                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7375
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 22                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 24                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.90
 p-value of test no 26                 :    0.03
 
 Stat. AD after spacings (mNP2-S)      :    0.92
 p-value of test no 27                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.73
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 29                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 32                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 34                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.72
 p-value of test no 35                 :    0.54
 
 Test on the Nm values of W_{n,i}(mNP1):    1.49
 p-value of test no 36                 :    0.18
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     257
 p-value of test no 37                 :    0.9939
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 38                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    1.90
 p-value of test no 39                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 40                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 41                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 42                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.29
 p-value of test no 46                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.67
 p-value of test no 48                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.23
 p-value of test no 50                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.19
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.39
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.19
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  284.59
 p-value of test no 54                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  388.23
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1509.57
 p-value of test no 56                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7029.65
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.60
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 60                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   44.45
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.63
 p-value of test no 65                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.31
 p-value of test no 66                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.09
 p-value of test no 67                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5038.10
 p-value of test no 68                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45943
 p-value of test no 70                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869943
   j =  1                              :        399908119
   j =  2                              :            45933
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 71                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908437
   j =  2                              :            45777
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 72                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 74                 :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 77                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 78                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 80                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 81                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 83                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 86                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 87                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 88                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.96
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 94                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 97                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 100                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.40
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 102                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.73
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 107                :    0.49
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 108                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
 p-value of test no 109                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
 p-value of test no 112                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
 p-value of test no 113                :    0.98
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 114                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 115                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 116                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.63
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.27
 p-value of test no 119                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.89
 p-value of test no 120                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.25
 p-value of test no 121                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.34
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.36
 p-value of test no 123                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.46
 p-value of test no 124                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.45
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 126                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.07
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 131                :    0.59
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.09
 p-value of test no 133                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.15
 p-value of test no 134                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.54
 p-value of test no 136                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.77
 p-value of test no 137                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  127.79
 p-value of test no 141                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 143                :    0.30
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17462.59
 p-value of test no 145                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.04
 p-value of test no 146                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.89
 p-value of test no 147                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.76
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.17
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.62
 p-value of test no 150                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.85
 p-value of test no 151                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.72
 p-value of test no 152                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.08
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   41.68
 p-value of test no 154                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.33
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.63
 p-value of test no 156                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.24
 p-value of test no 157                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  491.66
 p-value of test no 158                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  169.38
 p-value of test no 159                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.01
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.55
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  178.83
 p-value of test no 162                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  482.86
 p-value of test no 163                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.96
 p-value of test no 164                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.86
 p-value of test no 165                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.68
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.93
 p-value of test no 167                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5078.18
 p-value of test no 168                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  380.15
 p-value of test no 169                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  190.73
 p-value of test no 170                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.19
 p-value of test no 171                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.80
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5030.25
 p-value of test no 173                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  360.18
 p-value of test no 174                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.42
 p-value of test no 175                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.87
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.78
 p-value of test no 178                :    0.55
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.39
 p-value of test no 179                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 181                :    0.87
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 182                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.96
 p-value of test no 183                :    0.83
 
 Sample variance                       :    1.59
 p-value of test no 184                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.58
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 187                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.69
 p-value of test no 189                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 192                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.46
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.04
 p-value of test no 198                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 202                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  177.21
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 206                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.92
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 208                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 209                :    0.97
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9725.64
 p-value of test no 211                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9902.60
 p-value of test no 215                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.95
 p-value of test no 216                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 217                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.19
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 219                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 221                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.23
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.43
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 225                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4888.30
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.92
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4168.95
 p-value of test no 228                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11463.91
 p-value of test no 229                :    0.9911
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11891.52
 p-value of test no 230                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.43
 p-value of test no 231                :    0.85
 
 
 -----------------------------------------------
 Total number of bits:  7999977948
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.23
 p-value of test no 233                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999969869
 
 Normal statistic for number of bits   :   -0.24
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.46
 p-value of test no 238                :    0.68
 
 Sample variance                       :    1.60
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 240                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 242                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.69
 p-value of test no 243                :    0.95
 
 Sample variance                       :    1.31
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.17
 p-value of test no 248                :    0.57
 
 Sample variance                       :    0.59
 p-value of test no 249                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 253                :    0.30
 
 Sample variance                       :    1.00
 p-value of test no 254                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:31.71
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35949
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 4                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 6                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 7                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1319
 p-value of test no 10                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334439
   j =  1                              :        599997362
   j =  2                              :             1319
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1250
 p-value of test no 11                 :    0.9991    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334370
   j =  1                              :        599997500
   j =  2                              :             1250
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1473
 p-value of test no 12                 :  1.9e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334593
   j =  1                              :        599997054
   j =  2                              :             1473
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5209
 p-value of test no 13                 :    0.9981
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4390
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 15                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4331
 p-value of test no 16                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 17                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 18                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.76
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     921
 p-value of test no 25                 :    0.25
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 26                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.40
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 28                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 30                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 33                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 34                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 35                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 36                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     293
 p-value of test no 37                 :    0.64
 
 Stat. AD (mNP2)                       :    2.49
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 39                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.10
 p-value of test no 41                 :    0.30
 
 Test on the Nm values of W_{n,i}(mNP1):    2.27
 p-value of test no 42                 :    0.07
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 44                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.38
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.53
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.30
 p-value of test no 48                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.26
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.57
 p-value of test no 50                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.17
 p-value of test no 51                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   75.69
 p-value of test no 52                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.06
 p-value of test no 53                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  245.78
 p-value of test no 54                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.53
 p-value of test no 55                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1440.37
 p-value of test no 56                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6970.41
 p-value of test no 57                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 58                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.44
 p-value of test no 60                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   41.81
 p-value of test no 61                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 63                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 64                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.10
 p-value of test no 65                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.11
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.28
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4968.70
 p-value of test no 68                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45894
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869894
   j =  1                              :        399908214
   j =  2                              :            45890
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45935
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869935
   j =  1                              :        399908134
   j =  2                              :            45927
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 78                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 80                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 81                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 83                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 85                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 88                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.56
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 92                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 93                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 95                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 101                :    0.50
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 102                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 104                :    0.82
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 111                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
 p-value of test no 112                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 114                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 116                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 117                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 118                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.29
 p-value of test no 119                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.32
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.60
 p-value of test no 121                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.16
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.84
 p-value of test no 123                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.02
 p-value of test no 124                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.16
 p-value of test no 125                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 128                :    0.9905
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.58
 p-value of test no 129                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 130                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 132                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.41
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.81
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.55
 p-value of test no 135                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.90
 p-value of test no 136                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 137                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 140                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.50
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 142                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.55
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17406.04
 p-value of test no 145                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.75
 p-value of test no 146                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.86
 p-value of test no 147                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.41
 p-value of test no 148                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.90
 p-value of test no 149                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.32
 p-value of test no 150                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.84
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.18
 p-value of test no 152                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.81
 p-value of test no 153                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   37.68
 p-value of test no 154                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.64
 p-value of test no 155                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.98
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.71
 p-value of test no 157                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  449.16
 p-value of test no 158                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.65
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   94.08
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.75
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.37
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.81
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  178.45
 p-value of test no 164                :  8.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   41.80
 p-value of test no 165                :    0.9991    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.63
 p-value of test no 166                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.69
 p-value of test no 167                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5114.55
 p-value of test no 168                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.84
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.24
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.56
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.48
 p-value of test no 172                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4900.83
 p-value of test no 173                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  347.37
 p-value of test no 174                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.04
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.25
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.30
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.19
 p-value of test no 178                :    0.91
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.37
 p-value of test no 179                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 180                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.18
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 182                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.23
 p-value of test no 183                :    0.11
 
 Sample variance                       :    0.68
 p-value of test no 184                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.18
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 187                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.81
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
 p-value of test no 190                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 195                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.00
 p-value of test no 196                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.36
 p-value of test no 198                :    0.24
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 200                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  215.01
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.80
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 208                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 209                :    0.02
 
 Anderson-Darling statistic = A2       :    2.99
 p-value of test no 210                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10316.76
 p-value of test no 211                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 212                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 213                :    0.96
 
 Anderson-Darling statistic = A2       :    2.78
 p-value of test no 214                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9705.93
 p-value of test no 215                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.21
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.36
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 218                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4883.15
 p-value of test no 222                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 225                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4769.18
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.65
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4212.63
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11595.36
 p-value of test no 229                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12189.54
 p-value of test no 230                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.39
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999918368
 
 Normal statistic for number of bits   :   -0.65
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.32
 p-value of test no 233                :    0.79
 
 
 -----------------------------------------------
 Total number of bits:  8000147775
 
 Normal statistic for number of bits   :    1.17
 p-value of test no 234                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 236                :    0.79
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 237                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 238                :    0.86
 
 Sample variance                       :    1.56
 p-value of test no 239                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 241                :    0.81
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 242                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.12
 p-value of test no 244                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 245                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
 p-value of test no 246                :    0.9983
 
 Anderson-Darling statistic = A2       :    3.28
 p-value of test no 247                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.53
 p-value of test no 248                :    0.9943
 
 Sample variance                       :    1.44
 p-value of test no 249                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 251                :    0.87
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 252                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 253                :    0.75
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:31.98
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9991 
  77  RandomWalk1 C (L=1000, r=20)    0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35950
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 3                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 6                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 7                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 9                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 12                 :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5483
 p-value of test no 13                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4363
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7423
 p-value of test no 15                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 16                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7203
 p-value of test no 19                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 20                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 22                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 23                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    0.79
 p-value of test no 26                 :    0.49
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.66
 p-value of test no 28                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 29                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.31
 p-value of test no 30                 :    0.93
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.22
 p-value of test no 34                 :    0.26
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 35                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 36                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     311
 p-value of test no 37                 :    0.27
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 39                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 40                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 41                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    1.84
 p-value of test no 45                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:28.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.85
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.70
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.18
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.87
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.18
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.20
 p-value of test no 52                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.38
 p-value of test no 53                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  230.57
 p-value of test no 54                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  428.95
 p-value of test no 55                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1441.87
 p-value of test no 56                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7036.17
 p-value of test no 57                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.66
 p-value of test no 59                 :  6.0e-3
 
 Anderson-Darling statistic = A2       :    3.85
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   49.32
 p-value of test no 61                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 62                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 63                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 64                 :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   54.64
 p-value of test no 65                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.14
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.72
 p-value of test no 67                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5077.65
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908451
   j =  2                              :            45773
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46080
 p-value of test no 71                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870080
   j =  1                              :        399907845
   j =  2                              :            46070
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 74                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 77                 :    0.76
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 78                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 79                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 81                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 83                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.62
 p-value of test no 85                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 86                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 88                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.42
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 91                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 92                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 94                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 95                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 99                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 102                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 104                :    0.72
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 105                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 106                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 107                :    0.93
 
 Anderson-Darling statistic = A2       :    2.39
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
 p-value of test no 109                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
 p-value of test no 110                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
 p-value of test no 113                :    0.05
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 114                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 115                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.91
 p-value of test no 116                :  4.7e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.25
 p-value of test no 117                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.06
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.26
 p-value of test no 119                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.13
 p-value of test no 120                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.05
 p-value of test no 121                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.06
 p-value of test no 122                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.74
 p-value of test no 123                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.34
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.02
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 126                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 127                :    0.83
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 132                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.74
 p-value of test no 133                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.06
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.46
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 136                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.23
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 139                :    0.98
 
 Anderson-Darling statistic = A2       :    1.40
 p-value of test no 140                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.15
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 142                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.42
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 144                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.13
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.46
 p-value of test no 146                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.49
 p-value of test no 147                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.08
 p-value of test no 148                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   33.08
 p-value of test no 149                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.64
 p-value of test no 150                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.50
 p-value of test no 151                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.92
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.95
 p-value of test no 153                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.83
 p-value of test no 154                :    0.9901
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.35
 p-value of test no 155                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.47
 p-value of test no 156                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.66
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.57
 p-value of test no 158                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.09
 p-value of test no 159                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.44
 p-value of test no 160                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  120.52
 p-value of test no 161                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.70
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.76
 p-value of test no 163                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  137.59
 p-value of test no 164                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.71
 p-value of test no 165                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.09
 p-value of test no 166                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.85
 p-value of test no 167                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4988.42
 p-value of test no 168                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  367.30
 p-value of test no 169                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.97
 p-value of test no 170                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.77
 p-value of test no 171                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.80
 p-value of test no 172                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.41
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  441.83
 p-value of test no 174                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  180.43
 p-value of test no 175                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.66
 p-value of test no 176                :    0.26
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.48
 p-value of test no 177                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.15
 p-value of test no 178                :    0.11
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.088
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 183                :    0.71
 
 Sample variance                       :    0.32
 p-value of test no 184                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 186                :    0.90
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.64
 p-value of test no 188                :    0.74
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-3
 p-value of test no 191                :    0.99
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
 p-value of test no 194                :    0.46
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 195                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.74
 p-value of test no 196                :    0.12
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.34
 p-value of test no 198                :    0.50
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 202                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.70
 p-value of test no 203                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 204                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 205                :    0.19
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 206                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  212.83
 p-value of test no 207                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 209                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 210                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9968.38
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 212                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 213                :    0.13
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 214                :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10173.23
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.22
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 218                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 219                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 221                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4887.60
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 225                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4849.67
 p-value of test no 226                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4082.47
 p-value of test no 227                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4153.14
 p-value of test no 228                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.94
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11724.76
 p-value of test no 230                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   79.67
 p-value of test no 231                :    0.01
 
 
 -----------------------------------------------
 Total number of bits:  8000111898
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.99
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000001129
 
 Normal statistic for number of bits   : 8.93e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 237                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 238                :    0.57
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 242                :    0.9978
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.10
 p-value of test no 243                :    0.46
 
 Sample variance                       :    0.82
 p-value of test no 244                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 247                :    0.53
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.043
 p-value of test no 248                :    0.48
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.13
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 252                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.10
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.47
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:27.85
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  56  SampleCorr, k = 2               4.7e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35951
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1310
 p-value of test no 3                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334430
   j =  1                              :        599997380
   j =  2                              :             1310
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 5                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 6                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 8                  :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 10                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 12                 :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5317
 p-value of test no 13                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4442
 p-value of test no 14                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7379
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4393
 p-value of test no 16                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4385
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 18                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7286
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7206
 p-value of test no 21                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.52
 p-value of test no 23                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 26                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 27                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 30                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    0.50
 p-value of test no 32                 :    0.74
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 34                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.71
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 36                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 38                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    0.80
 p-value of test no 39                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 40                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.93
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 42                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     166
 p-value of test no 43                 :    0.10
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 44                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    0.65
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.61
 p-value of test no 46                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.47
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   10.97
 p-value of test no 48                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.27
 p-value of test no 49                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.12
 p-value of test no 50                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.49
 p-value of test no 51                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.74
 p-value of test no 52                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.52
 p-value of test no 53                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  259.72
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  421.52
 p-value of test no 55                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1501.50
 p-value of test no 56                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6825.40
 p-value of test no 57                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 58                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.59
 p-value of test no 59                 :    0.02
 
 Anderson-Darling statistic = A2       :    4.72
 p-value of test no 60                 :  4.3e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.98
 p-value of test no 61                 :  3.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   78.80
 p-value of test no 65                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.49
 p-value of test no 66                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  134.69
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5124.96
 p-value of test no 68                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45376
 p-value of test no 70                 :    0.9907
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869376
   j =  1                              :        399909248
   j =  2                              :            45376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45663
 p-value of test no 71                 :    0.84
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869663
   j =  1                              :        399908679
   j =  2                              :            45653
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 72                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 73                 :    0.01
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 74                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.02
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 83                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 84                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 87                 :    0.65
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 88                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 90                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 93                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 95                 :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 99                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 100                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 101                :    0.47
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 102                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.49
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
 p-value of test no 109                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
 p-value of test no 110                :    0.60
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 111                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
 p-value of test no 112                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 115                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.21
 p-value of test no 116                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 117                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   96.56
 p-value of test no 119                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.65
 p-value of test no 120                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.09
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.82
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.02
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.70
 p-value of test no 124                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.73
 p-value of test no 125                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 127                :    0.89
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.06
 p-value of test no 129                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 132                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.27
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.82
 p-value of test no 135                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 136                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.54
 p-value of test no 137                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 139                :    0.51
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 140                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  123.79
 p-value of test no 141                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17749.08
 p-value of test no 145                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.14
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.79
 p-value of test no 147                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.41
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.46
 p-value of test no 149                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.73
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.30
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.20
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.58
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.14
 p-value of test no 154                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.67
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.64
 p-value of test no 156                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.89
 p-value of test no 157                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  553.96
 p-value of test no 158                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.70
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.96
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  181.80
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.61
 p-value of test no 162                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.13
 p-value of test no 163                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  146.54
 p-value of test no 164                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   92.06
 p-value of test no 165                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.85
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.91
 p-value of test no 167                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4935.24
 p-value of test no 168                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.96
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  156.41
 p-value of test no 170                :    0.9900
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.25
 p-value of test no 171                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.86
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5053.92
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.98
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  182.65
 p-value of test no 175                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.23
 p-value of test no 176                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.44
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.15
 p-value of test no 179                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.58
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 182                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 183                :    0.55
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.57
 p-value of test no 185                :  6.7e-4    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 186                :    0.85
 
 Anderson-Darling statistic = A2       :    6.20
 p-value of test no 187                :  8.5e-4    *****
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.14
 p-value of test no 188                :    0.9992    *****
 
 Sample variance                       :    1.69
 p-value of test no 189                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.27
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.34
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.45
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 202                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  191.19
 p-value of test no 203                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 204                :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 205                :    0.97
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 206                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  156.50
 p-value of test no 207                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 209                :    0.41
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10039.12
 p-value of test no 211                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 213                :    0.87
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9950.21
 p-value of test no 215                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 217                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.68
 p-value of test no 218                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 219                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.23
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4914.25
 p-value of test no 222                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.05
 p-value of test no 226                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4083.58
 p-value of test no 227                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4113.81
 p-value of test no 228                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11738.70
 p-value of test no 229                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.90
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.84
 p-value of test no 231                :    0.81
 
 
 -----------------------------------------------
 Total number of bits:  7999924611
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   41.90
 p-value of test no 233                :    0.88
 
 
 -----------------------------------------------
 Total number of bits:  8000086122
 
 Normal statistic for number of bits   :    0.68
 p-value of test no 234                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 235                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 236                :    0.70
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.28
 p-value of test no 238                :    0.61
 
 Sample variance                       :    0.84
 p-value of test no 239                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 241                :    0.90
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.68
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.39
 p-value of test no 244                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.74
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 247                :    0.9910
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.16
 p-value of test no 248                :    0.44
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.26
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 252                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.94
 p-value of test no 253                :    0.17
 
 Sample variance                       :    0.54
 p-value of test no 254                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.01
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:17.61
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  83  LempelZiv, r = 15               0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35952
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 4                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1272
 p-value of test no 5                  :    0.9939
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334392
   j =  1                              :        599997456
   j =  2                              :             1272
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 9                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1445
 p-value of test no 11                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334565
   j =  1                              :        599997110
   j =  2                              :             1445
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5326
 p-value of test no 13                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 16                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4370
 p-value of test no 17                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7377
 p-value of test no 18                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7448
 p-value of test no 21                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.11
 p-value of test no 24                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     950
 p-value of test no 25                 :    0.05
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    1.51
 p-value of test no 27                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.06
 p-value of test no 29                 :    0.33
 
 Test on the Nm values of W_{n,i}(mNP1):    0.70
 p-value of test no 30                 :    0.56
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     612
 p-value of test no 31                 :    0.32
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 32                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 34                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 36                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     279
 p-value of test no 37                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.16
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.77
 p-value of test no 41                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 42                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     144
 p-value of test no 43                 :    0.67
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 44                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.95
 p-value of test no 46                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.05
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.08
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.41
 p-value of test no 49                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.02
 p-value of test no 50                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 51                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   78.44
 p-value of test no 52                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.25
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.43
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.63
 p-value of test no 55                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1408.13
 p-value of test no 56                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6891.48
 p-value of test no 57                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 60                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.59
 p-value of test no 61                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.02
 p-value of test no 65                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.03
 p-value of test no 66                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.17
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4990.12
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46239
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870239
   j =  1                              :        399907530
   j =  2                              :            46223
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45858
 p-value of test no 71                 :    0.54
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869858
   j =  1                              :        399908286
   j =  2                              :            45854
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 72                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 81                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.35
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 85                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 87                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 93                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 95                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 99                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 101                :    0.85
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 102                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 104                :    0.9939
 
 Anderson-Darling statistic = A2       :    5.18
 p-value of test no 105                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 106                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 108                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
 p-value of test no 109                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
 p-value of test no 110                :    0.11
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 114                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 115                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.80
 p-value of test no 119                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.89
 p-value of test no 120                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   47.71
 p-value of test no 121                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.19
 p-value of test no 122                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.38
 p-value of test no 123                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.11
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.55
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 127                :    0.91
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 128                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.46
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.97
 p-value of test no 133                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.60
 p-value of test no 134                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 137                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.90
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 143                :    0.35
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17473.61
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   77.17
 p-value of test no 146                :  7.9e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.37
 p-value of test no 147                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.81
 p-value of test no 148                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.46
 p-value of test no 149                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   33.55
 p-value of test no 150                :  9.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.70
 p-value of test no 151                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   24.61
 p-value of test no 152                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.55
 p-value of test no 153                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.23
 p-value of test no 154                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.28
 p-value of test no 155                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.24
 p-value of test no 156                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.73
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.47
 p-value of test no 158                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.19
 p-value of test no 159                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.86
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.09
 p-value of test no 161                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.27
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  466.47
 p-value of test no 163                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.53
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.88
 p-value of test no 165                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.37
 p-value of test no 166                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.14
 p-value of test no 167                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5174.53
 p-value of test no 168                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.12
 p-value of test no 169                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.65
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.77
 p-value of test no 171                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  384.40
 p-value of test no 172                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5045.69
 p-value of test no 173                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  405.45
 p-value of test no 174                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  178.02
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.80
 p-value of test no 176                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.43
 p-value of test no 178                :    0.75
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.96
 p-value of test no 183                :    0.17
 
 Sample variance                       :    1.99
 p-value of test no 184                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.35
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 187                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 188                :    0.24
 
 Sample variance                       :    0.58
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 4.57e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 195                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.10
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.82
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 201                :    0.96
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  169.85
 p-value of test no 203                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 206                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.33
 p-value of test no 207                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 210                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10263.87
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 214                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9979.91
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.10
 p-value of test no 216                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.014
 p-value of test no 217                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.40
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 219                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.26
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 221                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4833.98
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.41
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 225                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4962.64
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4181.32
 p-value of test no 227                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4156.06
 p-value of test no 228                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.47
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12044.74
 p-value of test no 230                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.14
 p-value of test no 231                :    0.07
 
 
 -----------------------------------------------
 Total number of bits:  7999874745
 
 Normal statistic for number of bits   :   -0.99
 p-value of test no 232                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.66
 p-value of test no 233                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000028066
 
 Normal statistic for number of bits   :    0.22
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 236                :    0.84
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 237                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 238                :    0.82
 
 Sample variance                       :    1.25
 p-value of test no 239                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.49
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 242                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.28
 p-value of test no 244                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 248                :    0.62
 
 Sample variance                       :    0.69
 p-value of test no 249                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 250                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.34
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 252                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.35
 p-value of test no 253                :    0.09
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:44.80
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  74  RandomWalk1 H (L=50, r=0)       7.9e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35953
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 3                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 4                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:15.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1291
 p-value of test no 7                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334411
   j =  1                              :        599997418
   j =  2                              :             1291
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 8                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 9                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 12                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5468
 p-value of test no 13                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7194
 p-value of test no 15                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4437
 p-value of test no 16                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4268
 p-value of test no 17                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 19                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7354
 p-value of test no 20                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7256
 p-value of test no 21                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.86
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.61
 p-value of test no 23                 :    0.04
 
 Test on the Nm values of W_{n,i}(mNP1):    9.67
 p-value of test no 24                 :  2.0e-5    *****
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     811
 p-value of test no 25                 :    0.9986
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 26                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.41
 p-value of test no 27                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 28                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 30                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     605
 p-value of test no 31                 :    0.42
 
 Stat. AD (mNP2)                       :    3.63
 p-value of test no 32                 :    0.01
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 35                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 36                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     297
 p-value of test no 37                 :    0.55
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    0.46
 p-value of test no 39                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.50
 p-value of test no 40                 :    0.74
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.33
 p-value of test no 42                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     152
 p-value of test no 43                 :    0.45
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.14
 p-value of test no 45                 :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.19
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.73
 p-value of test no 47                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.27
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   39.27
 p-value of test no 49                 :  2.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.98
 p-value of test no 50                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.53
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.46
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.61
 p-value of test no 53                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.31
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  430.62
 p-value of test no 55                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1424.47
 p-value of test no 56                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7087.49
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 59                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 60                 :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   47.39
 p-value of test no 61                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 62                 :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 63                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   71.59
 p-value of test no 65                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.16
 p-value of test no 66                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  102.51
 p-value of test no 67                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5126.63
 p-value of test no 68                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46072
 p-value of test no 70                 :    0.18
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870072
   j =  1                              :        399907858
   j =  2                              :            46068
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45936
 p-value of test no 71                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869936
   j =  1                              :        399908133
   j =  2                              :            45926
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 72                 :  2.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 73                 :    0.90
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 74                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 76                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 81                 :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.77
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 85                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 87                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 88                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 90                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 92                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 94                 :    0.91
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 98                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 100                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.86
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.90
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 105                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
 p-value of test no 110                :    0.86
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
 p-value of test no 113                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.48
 p-value of test no 118                :    0.9934
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.37
 p-value of test no 119                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.54
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.63
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.76
 p-value of test no 122                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.86
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.09
 p-value of test no 124                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.62
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 127                :    0.82
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 128                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.12
 p-value of test no 129                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 131                :    0.97
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.76
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.53
 p-value of test no 134                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.13
 p-value of test no 135                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.88
 p-value of test no 136                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 138                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.91
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.48
 p-value of test no 143                :  6.7e-3
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 144                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17831.98
 p-value of test no 145                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.03
 p-value of test no 146                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.42
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.00
 p-value of test no 148                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   10.18
 p-value of test no 149                :    0.9937
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.86
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   25.12
 p-value of test no 151                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   22.75
 p-value of test no 152                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.29
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.24
 p-value of test no 154                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.98
 p-value of test no 155                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.56
 p-value of test no 156                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.13
 p-value of test no 157                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.55
 p-value of test no 158                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  147.46
 p-value of test no 159                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  110.86
 p-value of test no 160                :  3.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.67
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.96
 p-value of test no 162                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  451.85
 p-value of test no 163                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.14
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.58
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.32
 p-value of test no 166                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  330.29
 p-value of test no 167                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.91
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  351.92
 p-value of test no 169                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.11
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.40
 p-value of test no 171                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.92
 p-value of test no 172                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4912.60
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  387.53
 p-value of test no 174                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.44
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.78
 p-value of test no 176                :    0.25
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.12
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.20
 p-value of test no 179                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.66
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 182                :    0.48
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 185                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 187                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    1.00
 p-value of test no 189                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
 p-value of test no 193                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 195                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.73
 p-value of test no 196                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.39
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 201                :    0.76
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.20
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  197.55
 p-value of test no 207                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 209                :    0.85
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 210                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9862.51
 p-value of test no 211                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 213                :    0.24
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 214                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.63
 p-value of test no 215                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.44
 p-value of test no 217                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 218                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 221                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4816.71
 p-value of test no 222                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 225                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4861.49
 p-value of test no 226                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3936.03
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4025.66
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12103.21
 p-value of test no 229                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12140.08
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.26
 p-value of test no 231                :    0.76
 
 
 -----------------------------------------------
 Total number of bits:  7999933959
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 232                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.54
 p-value of test no 233                :    0.53
 
 
 -----------------------------------------------
 Total number of bits:  8000052537
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.37
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.95
 p-value of test no 239                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 241                :    0.02
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 243                :    0.10
 
 Sample variance                       :    0.35
 p-value of test no 244                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 245                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.34
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 247                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.36
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 250                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
 p-value of test no 251                :    0.9972
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 252                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.57
 p-value of test no 253                :    0.9949
 
 Sample variance                       :    0.99
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:33.06
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs mNP1, t = 3          2.0e-5
  25  ClosePairs mNP2S, t = 16        0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35954
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 3                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 4                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5478
 p-value of test no 13                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 14                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7431
 p-value of test no 15                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7365
 p-value of test no 18                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 19                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7413
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 21                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    0.58
 p-value of test no 24                 :    0.66
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     873
 p-value of test no 25                 :    0.81
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 27                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.43
 p-value of test no 28                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 29                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 30                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.82
 p-value of test no 32                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    2.17
 p-value of test no 33                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 34                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.70
 p-value of test no 35                 :    0.55
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     281
 p-value of test no 37                 :    0.86
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.11
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.61
 p-value of test no 41                 :    0.63
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.48
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.99
 p-value of test no 46                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.59
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 48                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.78
 p-value of test no 49                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.40
 p-value of test no 50                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.91
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.95
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.92
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  269.69
 p-value of test no 54                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  491.09
 p-value of test no 55                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.19
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7028.37
 p-value of test no 57                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 60                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   22.48
 p-value of test no 61                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 63                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 64                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.56
 p-value of test no 65                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.40
 p-value of test no 66                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.63
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.27
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45808
 p-value of test no 70                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869808
   j =  1                              :        399908387
   j =  2                              :            45802
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 71                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908344
   j =  2                              :            45822
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 72                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 74                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 76                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 79                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 80                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 84                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 85                 :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 87                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 88                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 95                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 97                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 99                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 100                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.37
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.21
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 108                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
 p-value of test no 109                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
 p-value of test no 110                :    0.65
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 111                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
 p-value of test no 113                :    0.36
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 114                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 115                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.96
 p-value of test no 116                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 118                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.39
 p-value of test no 119                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.35
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.02
 p-value of test no 121                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   58.81
 p-value of test no 122                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.40
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.33
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.38
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.33
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.85
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 132                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.38
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.47
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.24
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.30
 p-value of test no 136                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.32
 p-value of test no 137                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 138                :  6.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    3.18
 p-value of test no 140                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  100.76
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 144                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17607.57
 p-value of test no 145                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.37
 p-value of test no 146                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   50.68
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.65
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.84
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.76
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.68
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.63
 p-value of test no 152                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   34.60
 p-value of test no 153                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.27
 p-value of test no 154                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.72
 p-value of test no 155                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.12
 p-value of test no 156                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.00
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.55
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  149.77
 p-value of test no 159                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.92
 p-value of test no 160                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.91
 p-value of test no 161                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.76
 p-value of test no 162                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.92
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.91
 p-value of test no 164                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  114.95
 p-value of test no 165                :  1.6e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  414.24
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.03
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5070.73
 p-value of test no 168                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.78
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  218.19
 p-value of test no 170                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  343.07
 p-value of test no 171                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  321.96
 p-value of test no 172                :    0.9906
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5147.87
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.42
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  222.06
 p-value of test no 175                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.89
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.45
 p-value of test no 177                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.54
 p-value of test no 178                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.49
 p-value of test no 179                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 181                :    0.57
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 182                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 183                :    0.69
 
 Sample variance                       :    1.75
 p-value of test no 184                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 187                :    0.38
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.39
 p-value of test no 188                :    0.92
 
 Sample variance                       :    1.22
 p-value of test no 189                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
 p-value of test no 191                :    0.69
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-3
 p-value of test no 193                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.13
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 195                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.17
 p-value of test no 196                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.19
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 201                :    0.33
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.28
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.50
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  200.65
 p-value of test no 207                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9884.84
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 212                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 213                :    0.97
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9803.38
 p-value of test no 215                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.57
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 218                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 221                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4896.96
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 224                :    0.97
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 225                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4744.02
 p-value of test no 226                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.54
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4049.98
 p-value of test no 228                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12041.13
 p-value of test no 229                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11774.59
 p-value of test no 230                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.40
 p-value of test no 231                :    0.32
 
 
 -----------------------------------------------
 Total number of bits:  8000062836
 
 Normal statistic for number of bits   :    0.50
 p-value of test no 232                :    0.31
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.66
 p-value of test no 233                :    0.45
 
 
 -----------------------------------------------
 Total number of bits:  8000029299
 
 Normal statistic for number of bits   :    0.23
 p-value of test no 234                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.15
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.73
 p-value of test no 238                :    0.23
 
 Sample variance                       :    0.25
 p-value of test no 239                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 242                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 243                :    0.64
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 245                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 246                :    0.94
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.77
 p-value of test no 248                :    0.96
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.21
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35955
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 4                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 5                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 7                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 10                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 11                 :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 12                 :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5347
 p-value of test no 13                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4349
 p-value of test no 14                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 15                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4233
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 17                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7177
 p-value of test no 18                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7277
 p-value of test no 19                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7348
 p-value of test no 20                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7419
 p-value of test no 21                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.41
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.35
 p-value of test no 24                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 26                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.50
 p-value of test no 27                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 28                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 32                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    2.36
 p-value of test no 33                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     316
 p-value of test no 37                 :    0.18
 
 Stat. AD (mNP2)                       :    1.51
 p-value of test no 38                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 39                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 40                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.89
 p-value of test no 41                 :    0.03
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 42                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     131
 p-value of test no 43                 :    0.94
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 44                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.51
 p-value of test no 46                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.12
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.03
 p-value of test no 48                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   30.08
 p-value of test no 49                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.48
 p-value of test no 50                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.56
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.20
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.26
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.39
 p-value of test no 54                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.57
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1608.22
 p-value of test no 56                 :  1.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7240.85
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 58                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   40.32
 p-value of test no 61                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 62                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 64                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.70
 p-value of test no 65                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.98
 p-value of test no 66                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  106.37
 p-value of test no 67                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5056.67
 p-value of test no 68                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46012
 p-value of test no 70                 :    0.27
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870012
   j =  1                              :        399907979
   j =  2                              :            46006
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45628
 p-value of test no 71                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869628
   j =  1                              :        399908749
   j =  2                              :            45618
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:05:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 72                 :  6.1e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    2.81
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.86
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 78                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 80                 :    0.71
 
 Anderson-Darling statistic = A2       :    1.53
 p-value of test no 81                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 85                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 86                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 90                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 94                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 97                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 98                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 99                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 100                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.13
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 102                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 103                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 104                :    0.63
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 105                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.18
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 108                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
 p-value of test no 109                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 110                :    0.57
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 111                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
 p-value of test no 112                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
 p-value of test no 113                :    0.16
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 114                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.39
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.16
 p-value of test no 116                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.66
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 118                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.43
 p-value of test no 119                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.59
 p-value of test no 120                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.43
 p-value of test no 121                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.33
 p-value of test no 122                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.50
 p-value of test no 123                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.57
 p-value of test no 124                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.35
 p-value of test no 125                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 128                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.25
 p-value of test no 129                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 131                :    0.92
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 132                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.10
 p-value of test no 133                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 134                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.04
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 139                :    0.99
 
 Anderson-Darling statistic = A2       :    2.12
 p-value of test no 140                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   99.40
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17493.18
 p-value of test no 145                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.60
 p-value of test no 146                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.58
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.14
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.22
 p-value of test no 149                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   28.70
 p-value of test no 150                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.78
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.01
 p-value of test no 152                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.85
 p-value of test no 153                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.08
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.87
 p-value of test no 155                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.96
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.44
 p-value of test no 157                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  527.37
 p-value of test no 158                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.52
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.77
 p-value of test no 160                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.44
 p-value of test no 161                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.17
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  531.64
 p-value of test no 163                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.71
 p-value of test no 164                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.22
 p-value of test no 165                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.05
 p-value of test no 166                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.17
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5102.74
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.77
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.78
 p-value of test no 170                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  425.85
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.18
 p-value of test no 172                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4905.12
 p-value of test no 173                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  408.18
 p-value of test no 174                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.66
 p-value of test no 175                :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.64
 p-value of test no 176                :    0.56
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.01
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.21
 p-value of test no 178                :    0.43
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 179                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 183                :    0.23
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 186                :    0.75
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 187                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.31
 p-value of test no 188                :    0.62
 
 Sample variance                       :    0.73
 p-value of test no 189                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
 p-value of test no 190                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
 p-value of test no 193                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.83
 p-value of test no 196                :    0.28
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.64
 p-value of test no 198                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 200                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 202                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.35
 p-value of test no 203                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 204                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 205                :    0.31
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  206.87
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9960.49
 p-value of test no 211                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 212                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.36
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 214                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10040.34
 p-value of test no 215                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.00
 p-value of test no 216                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.73
 p-value of test no 217                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.80
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 219                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 220                :    0.35
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 221                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4852.13
 p-value of test no 222                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.12
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4103.39
 p-value of test no 227                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.39
 p-value of test no 228                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11936.33
 p-value of test no 229                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12024.36
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   35.31
 p-value of test no 231                :    0.98
 
 
 -----------------------------------------------
 Total number of bits:  8000025258
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.52
 p-value of test no 233                :    0.57
 
 
 -----------------------------------------------
 Total number of bits:  7999824627
 
 Normal statistic for number of bits   :   -1.39
 p-value of test no 234                :    0.92
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 238                :    0.84
 
 Sample variance                       :    1.11
 p-value of test no 239                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 240                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 241                :    0.97
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 242                :    0.41
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    0.89
 p-value of test no 244                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.45
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 247                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 249                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 252                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 253                :    0.32
 
 Sample variance                       :    0.28
 p-value of test no 254                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:16.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35956
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 3                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 5                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 7                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 11                 :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 12                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4217
 p-value of test no 14                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 15                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 16                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7308
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7371
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7281
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 21                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.72
 p-value of test no 22                 :    0.54
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.36
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     864
 p-value of test no 25                 :    0.88
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 26                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 27                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.71
 p-value of test no 28                 :    0.04
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.91
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 30                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     590
 p-value of test no 31                 :    0.65
 
 Stat. AD (mNP2)                       :    2.56
 p-value of test no 32                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.48
 p-value of test no 33                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.78
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 35                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.18
 p-value of test no 36                 :    0.28
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 38                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 40                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.51
 p-value of test no 41                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 42                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 45                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   14.17
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.68
 p-value of test no 47                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.24
 p-value of test no 48                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   26.30
 p-value of test no 49                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.97
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.07
 p-value of test no 51                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.82
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.35
 p-value of test no 53                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  214.79
 p-value of test no 54                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  425.94
 p-value of test no 55                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1474.27
 p-value of test no 56                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6994.91
 p-value of test no 57                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.96
 p-value of test no 61                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 62                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.24
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.57
 p-value of test no 65                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.94
 p-value of test no 66                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.58
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4960.78
 p-value of test no 68                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45524
 p-value of test no 70                 :    0.95
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869524
   j =  1                              :        399908956
   j =  2                              :            45516
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45689
 p-value of test no 71                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869689
   j =  1                              :        399908626
   j =  2                              :            45681
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 73                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 80                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 83                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 84                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 85                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 88                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 91                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 94                 :    0.65
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.88
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 97                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 99                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 100                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 104                :    0.11
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 105                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 107                :    0.10
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.17e-5
 p-value of test no 109                :    0.9945
 
 Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
 p-value of test no 110                :    0.03
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
 p-value of test no 112                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 114                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.87
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 116                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.26
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.43
 p-value of test no 118                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.48
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.70
 p-value of test no 120                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.17
 p-value of test no 121                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.06
 p-value of test no 122                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.66
 p-value of test no 123                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.51
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.69
 p-value of test no 125                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 127                :    0.85
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 128                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.63
 p-value of test no 129                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.12
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 132                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.34
 p-value of test no 133                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.54
 p-value of test no 135                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 138                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 139                :    0.90
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  119.98
 p-value of test no 141                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 142                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 144                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17551.07
 p-value of test no 145                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.69
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.90
 p-value of test no 147                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.58
 p-value of test no 148                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   13.95
 p-value of test no 149                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.97
 p-value of test no 150                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.39
 p-value of test no 151                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.57
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.11
 p-value of test no 153                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.02
 p-value of test no 154                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.59
 p-value of test no 155                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.23
 p-value of test no 156                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.63
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.68
 p-value of test no 158                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.55
 p-value of test no 159                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.51
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.61
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.90
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  534.21
 p-value of test no 163                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.87
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.24
 p-value of test no 165                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.92
 p-value of test no 166                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.68
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4792.32
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.38
 p-value of test no 169                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.44
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.15
 p-value of test no 171                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.36
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4967.12
 p-value of test no 173                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.18
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.55
 p-value of test no 175                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.90
 p-value of test no 176                :    0.86
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 177                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.50
 p-value of test no 178                :    0.27
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.31
 p-value of test no 179                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 180                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 182                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 183                :    0.35
 
 Sample variance                       :    0.64
 p-value of test no 184                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.72
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.33
 p-value of test no 188                :    0.63
 
 Sample variance                       :    1.77
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
 p-value of test no 191                :    0.89
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 192                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 195                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.59
 p-value of test no 196                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   25.13
 p-value of test no 198                :  1.5e-3
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.40
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 202                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.90
 p-value of test no 203                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.80
 p-value of test no 207                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 209                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 210                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10077.43
 p-value of test no 211                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 213                :    0.78
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 214                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.43
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.15
 p-value of test no 216                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 217                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.68
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 221                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4874.27
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4956.86
 p-value of test no 226                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3975.45
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4247.46
 p-value of test no 228                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11845.62
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11730.84
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.10
 p-value of test no 231                :    0.19
 
 
 -----------------------------------------------
 Total number of bits:  8000015667
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 232                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.56
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000025066
 
 Normal statistic for number of bits   :    0.20
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 236                :  2.6e-3
 
 Anderson-Darling statistic = A2       :    4.07
 p-value of test no 237                :  8.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.50
 p-value of test no 238                :  6.2e-3
 
 Sample variance                       :    0.99
 p-value of test no 239                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 240                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 241                :    0.96
 
 Anderson-Darling statistic = A2       :    2.16
 p-value of test no 242                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.81
 p-value of test no 243                :    0.96
 
 Sample variance                       :    1.25
 p-value of test no 244                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 247                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 248                :    0.84
 
 Sample variance                       :    1.28
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 251                :    0.83
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 252                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.28
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.75
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35957
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 3                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 4                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 5                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 6                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 8                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 9                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 11                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 12                 :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5546
 p-value of test no 13                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4506
 p-value of test no 14                 :  5.4e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7350
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4359
 p-value of test no 17                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7253
 p-value of test no 18                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7328
 p-value of test no 20                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7694
 p-value of test no 21                 :  6.8e-6    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.59
 p-value of test no 22                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 23                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 24                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     912
 p-value of test no 25                 :    0.35
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 26                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    1.20
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.76
 p-value of test no 28                 :    0.51
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 29                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 30                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    1.69
 p-value of test no 32                 :    0.14
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 33                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 34                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     313
 p-value of test no 37                 :    0.23
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 40                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 41                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.72
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.82
 p-value of test no 46                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.94
 p-value of test no 47                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.07
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.14
 p-value of test no 49                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.67
 p-value of test no 50                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.34
 p-value of test no 51                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.02
 p-value of test no 52                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.33
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  256.49
 p-value of test no 54                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.64
 p-value of test no 55                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1378.19
 p-value of test no 56                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7161.93
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 59                 :    0.27
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 60                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   45.20
 p-value of test no 61                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 64                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   67.43
 p-value of test no 65                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.75
 p-value of test no 66                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  139.69
 p-value of test no 67                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5209.51
 p-value of test no 68                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46232
 p-value of test no 70                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870232
   j =  1                              :        399907538
   j =  2                              :            46228
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908591
   j =  2                              :            45697
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 73                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.14
 p-value of test no 74                 :    0.9994    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    1.89
 p-value of test no 81                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.94
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 84                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.41
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 92                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 93                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 94                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 95                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 97                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 98                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 100                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.19
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 102                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 105                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 106                :  4.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    3.22
 p-value of test no 108                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.75e-5
 p-value of test no 109                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
 p-value of test no 110                :    0.10
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 111                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
 p-value of test no 112                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 113                :    0.28
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 114                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 115                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.29
 p-value of test no 116                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 117                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.25
 p-value of test no 118                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   42.41
 p-value of test no 119                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.08
 p-value of test no 120                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   98.71
 p-value of test no 121                :  7.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.39
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.90
 p-value of test no 123                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.60
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.39
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 126                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.92
 p-value of test no 129                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 130                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 131                :    0.04
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.99
 p-value of test no 133                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.89
 p-value of test no 134                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.56
 p-value of test no 135                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.25
 p-value of test no 136                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.50
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 138                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  155.92
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 142                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.95
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.67
 p-value of test no 146                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.78
 p-value of test no 147                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.73
 p-value of test no 148                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   12.18
 p-value of test no 149                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.23
 p-value of test no 150                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.98
 p-value of test no 152                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.51
 p-value of test no 153                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.26
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.69
 p-value of test no 155                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  158.75
 p-value of test no 156                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.08
 p-value of test no 157                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.19
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.76
 p-value of test no 159                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.79
 p-value of test no 160                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.12
 p-value of test no 161                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.42
 p-value of test no 162                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  455.45
 p-value of test no 163                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  143.03
 p-value of test no 164                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   80.67
 p-value of test no 165                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.77
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  406.10
 p-value of test no 167                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.43
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  362.77
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.69
 p-value of test no 170                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.67
 p-value of test no 171                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.81
 p-value of test no 172                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.32
 p-value of test no 173                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.17
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.54
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.95
 p-value of test no 176                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : 2.98e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.99
 p-value of test no 178                :    0.45
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.84
 p-value of test no 179                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.33
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 187                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.38
 p-value of test no 188                :    0.35
 
 Sample variance                       :    2.45
 p-value of test no 189                :  8.7e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
 p-value of test no 191                :    0.80
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 192                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
 p-value of test no 193                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
 p-value of test no 194                :    0.48
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.56
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.33
 p-value of test no 198                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 201                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  213.71
 p-value of test no 203                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 205                :    0.90
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.29
 p-value of test no 207                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.74
 p-value of test no 211                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.65
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9981.48
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.40
 p-value of test no 216                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.86
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4919.24
 p-value of test no 222                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 223                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 224                :    0.24
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 225                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4934.92
 p-value of test no 226                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4072.54
 p-value of test no 227                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4090.14
 p-value of test no 228                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11768.52
 p-value of test no 229                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11999.22
 p-value of test no 230                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.14
 p-value of test no 231                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999926771
 
 Normal statistic for number of bits   :   -0.58
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   90.50
 p-value of test no 233                :  1.4e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999994202
 
 Normal statistic for number of bits   :  -0.046
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 235                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.69
 p-value of test no 239                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 241                :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 242                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.42
 p-value of test no 243                :    0.34
 
 Sample variance                       :    1.84
 p-value of test no 244                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 245                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.66
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.062
 p-value of test no 248                :    0.52
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 252                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.69
 
 Sample variance                       :    1.64
 p-value of test no 254                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.10
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:33.65
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  21  BirthdaySpacings, t = 16        6.8e-6
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35958
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 3                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 4                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1298
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334418
   j =  1                              :        599997404
   j =  2                              :             1298
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 6                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 8                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 10                 :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1330
 p-value of test no 11                 :    0.82
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334450
   j =  1                              :        599997340
   j =  2                              :             1330
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 12                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5292
 p-value of test no 13                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 14                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7337
 p-value of test no 15                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7490
 p-value of test no 18                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7231
 p-value of test no 19                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 21                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 22                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.37
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    2.40
 p-value of test no 24                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     858
 p-value of test no 25                 :    0.92
 
 Stat. AD (mNP2)                       :    2.02
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 27                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.82
 p-value of test no 28                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 30                 :    0.77
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     586
 p-value of test no 31                 :    0.71
 
 Stat. AD (mNP2)                       :    1.33
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    0.84
 p-value of test no 33                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.56
 p-value of test no 34                 :    0.05
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.76
 p-value of test no 35                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     317
 p-value of test no 37                 :    0.17
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 38                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.58
 p-value of test no 39                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 42                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     158
 p-value of test no 43                 :    0.27
 
 Stat. AD (mNP2)                       :    0.35
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.52
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.54
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.51
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.50
 p-value of test no 49                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.21
 p-value of test no 50                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.02
 p-value of test no 51                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.16
 p-value of test no 52                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.90
 p-value of test no 53                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.83
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  486.06
 p-value of test no 55                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1361.76
 p-value of test no 56                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7172.95
 p-value of test no 57                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.51
 p-value of test no 58                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 59                 :    0.97
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.57
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.26
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.25
 p-value of test no 66                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  135.32
 p-value of test no 67                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4989.03
 p-value of test no 68                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45708
 p-value of test no 70                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869708
   j =  1                              :        399908591
   j =  2                              :            45694
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46284
 p-value of test no 71                 :    0.03
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870284
   j =  1                              :        399907433
   j =  2                              :            46282
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 72                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 73                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 74                 :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 79                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 81                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 88                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.20
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 93                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 95                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 100                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 101                :    0.04
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 104                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 108                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 109                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
 p-value of test no 112                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    : 3.09e-5
 p-value of test no 113                :    0.96
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 115                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    3.07
 p-value of test no 116                :  1.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.27
 p-value of test no 117                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 118                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.83
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.78
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.41
 p-value of test no 121                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.80
 p-value of test no 122                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.84
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.23
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.61
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.13
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 128                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   52.24
 p-value of test no 129                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
 p-value of test no 130                :    0.9954
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 132                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   59.19
 p-value of test no 133                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.44
 p-value of test no 134                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 139                :    0.29
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 140                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  139.72
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 143                :    0.83
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 144                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17217.73
 p-value of test no 145                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.29
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.18
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.99
 p-value of test no 148                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.88
 p-value of test no 149                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.82
 p-value of test no 150                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   46.96
 p-value of test no 151                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.03
 p-value of test no 152                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.97
 p-value of test no 153                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.61
 p-value of test no 154                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.76
 p-value of test no 155                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.37
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  110.81
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  472.00
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.72
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   59.81
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.88
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.25
 p-value of test no 162                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.05
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.50
 p-value of test no 164                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.37
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.24
 p-value of test no 166                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  362.53
 p-value of test no 167                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.29
 p-value of test no 168                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  357.69
 p-value of test no 169                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  209.87
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.53
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.91
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5007.55
 p-value of test no 173                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.24
 p-value of test no 174                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  170.24
 p-value of test no 175                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.37
 p-value of test no 176                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.16
 p-value of test no 177                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.11
 p-value of test no 178                :    0.29
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.02
 p-value of test no 179                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 181                :    0.54
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 182                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 183                :    0.77
 
 Sample variance                       :    1.46
 p-value of test no 184                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 186                :    0.07
 
 Anderson-Darling statistic = A2       :    2.37
 p-value of test no 187                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.58
 p-value of test no 188                :    0.06
 
 Sample variance                       :    2.45
 p-value of test no 189                :  8.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
 p-value of test no 190                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 191                :    0.21
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 192                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
 p-value of test no 193                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.020
 p-value of test no 194                :    0.04
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.22
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.23
 p-value of test no 198                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 200                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.47
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.91
 p-value of test no 203                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.67
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 206                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.77
 p-value of test no 207                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 209                :    0.90
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 210                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9845.55
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 212                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 214                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9827.50
 p-value of test no 215                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.31
 p-value of test no 216                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 217                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.08
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 221                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4912.92
 p-value of test no 222                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 223                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 224                :    0.73
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 225                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4812.23
 p-value of test no 226                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4059.77
 p-value of test no 227                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4115.51
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11962.82
 p-value of test no 229                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.82
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   73.86
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  8000046873
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.51
 p-value of test no 233                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999901850
 
 Normal statistic for number of bits   :   -0.78
 p-value of test no 234                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 237                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 238                :    0.55
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 240                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 241                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 242                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 243                :    0.19
 
 Sample variance                       :    1.67
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 245                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 246                :    0.86
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 247                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.32
 p-value of test no 248                :    0.91
 
 Sample variance                       :    0.39
 p-value of test no 249                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.26
 p-value of test no 253                :    0.40
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:59.07
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35959
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1338
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334458
   j =  1                              :        599997324
   j =  2                              :             1338
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 5                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1277
 p-value of test no 6                  :    0.9911
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334397
   j =  1                              :        599997446
   j =  2                              :             1277
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 7                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 9                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1396
 p-value of test no 10                 :    0.20
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334516
   j =  1                              :        599997208
   j =  2                              :             1396
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 11                 :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5403
 p-value of test no 13                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7215
 p-value of test no 15                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 16                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7456
 p-value of test no 19                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7452
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 21                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.64
 p-value of test no 23                 :    0.61
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 24                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     896
 p-value of test no 25                 :    0.54
 
 Stat. AD (mNP2)                       :    1.98
 p-value of test no 26                 :    0.09
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 27                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.39
 p-value of test no 28                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.67
 p-value of test no 29                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 30                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 32                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.05
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.18
 p-value of test no 34                 :    0.9946
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    3.35
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     248
 p-value of test no 37                 :    0.9989
 
 Stat. AD (mNP2)                       :    1.89
 p-value of test no 38                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 39                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 40                 :    0.63
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.09
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 42                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.52
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.06
 p-value of test no 46                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.61
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.37
 p-value of test no 48                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.75
 p-value of test no 49                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.34
 p-value of test no 50                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.75
 p-value of test no 51                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.40
 p-value of test no 52                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.93
 p-value of test no 53                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  196.70
 p-value of test no 54                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.95
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1410.88
 p-value of test no 56                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6963.64
 p-value of test no 57                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 58                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 59                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 60                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.97
 p-value of test no 61                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 62                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.63
 p-value of test no 65                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.92
 p-value of test no 67                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5130.74
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9971
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45730
 p-value of test no 70                 :    0.76
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869730
   j =  1                              :        399908542
   j =  2                              :            45726
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45980
 p-value of test no 71                 :    0.32
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869980
   j =  1                              :        399908045
   j =  2                              :            45970
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 74                 :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
 p-value of test no 76                 :    0.9934
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.85
 p-value of test no 78                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 80                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 83                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 85                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 86                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 87                 :    0.66
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.84
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 91                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 92                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 94                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.61
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 100                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 101                :    0.14
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 102                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.33
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 105                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 108                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
 p-value of test no 109                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
 p-value of test no 110                :    0.74
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
 p-value of test no 113                :    0.07
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 114                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.82
 p-value of test no 115                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 117                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.82
 p-value of test no 119                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.22
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.87
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.72
 p-value of test no 122                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.35
 p-value of test no 123                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.18
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.67
 p-value of test no 129                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.70
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 132                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.87
 p-value of test no 133                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.05
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.45
 p-value of test no 135                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.84
 p-value of test no 136                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 138                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 139                :    0.04
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 140                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  149.21
 p-value of test no 141                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 142                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.73
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 144                :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17264.51
 p-value of test no 145                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.60
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.24
 p-value of test no 147                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.46
 p-value of test no 148                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.14
 p-value of test no 149                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.92
 p-value of test no 151                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.19
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.81
 p-value of test no 153                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.92
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.25
 p-value of test no 155                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  115.42
 p-value of test no 156                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.21
 p-value of test no 157                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.95
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.97
 p-value of test no 159                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.65
 p-value of test no 160                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.20
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.18
 p-value of test no 162                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  416.78
 p-value of test no 163                :    0.9972
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  176.17
 p-value of test no 164                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.06
 p-value of test no 165                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.46
 p-value of test no 166                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  318.83
 p-value of test no 167                :    0.9933
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5033.71
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  327.04
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  174.41
 p-value of test no 170                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.83
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.88
 p-value of test no 172                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5037.22
 p-value of test no 173                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.49
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  213.84
 p-value of test no 175                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.26
 p-value of test no 176                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.32
 p-value of test no 177                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.82
 p-value of test no 178                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 180                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.26
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 185                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.038
 p-value of test no 188                :    0.48
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 192                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
 p-value of test no 193                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.67
 p-value of test no 196                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.02
 p-value of test no 198                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 201                :    0.04
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 202                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  229.42
 p-value of test no 203                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 205                :    0.48
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 206                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.94
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.15
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 210                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10059.72
 p-value of test no 211                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.50
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10096.07
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.54
 p-value of test no 217                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.46
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.58
 p-value of test no 222                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 224                :    0.07
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 225                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4930.19
 p-value of test no 226                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4122.45
 p-value of test no 227                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.52
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11921.16
 p-value of test no 229                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11629.87
 p-value of test no 230                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   43.57
 p-value of test no 231                :    0.84
 
 
 -----------------------------------------------
 Total number of bits:  8000047170
 
 Normal statistic for number of bits   :    0.37
 p-value of test no 232                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.85
 p-value of test no 233                :    0.60
 
 
 -----------------------------------------------
 Total number of bits:  8000031252
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 237                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.90
 p-value of test no 238                :    0.18
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 240                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 242                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.07
 p-value of test no 243                :    0.14
 
 Sample variance                       :    0.41
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 245                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 246                :    0.03
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.50
 p-value of test no 248                :    0.07
 
 Sample variance                       :    0.50
 p-value of test no 249                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 251                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.45
 p-value of test no 254                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.05
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:46.50
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35960
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 3                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1294
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334414
   j =  1                              :        599997412
   j =  2                              :             1294
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 6                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 7                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 10                 :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 11                 :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 12                 :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4432
 p-value of test no 14                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 15                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4490
 p-value of test no 16                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7293
 p-value of test no 18                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7410
 p-value of test no 19                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7084
 p-value of test no 20                 :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7223
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.16
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 23                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    2.44
 p-value of test no 24                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     849
 p-value of test no 25                 :    0.95
 
 Stat. AD (mNP2)                       :    0.43
 p-value of test no 26                 :    0.82
 
 Stat. AD after spacings (mNP2-S)      :    1.60
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.99
 p-value of test no 28                 :    0.36
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.96
 p-value of test no 29                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    1.28
 p-value of test no 32                 :    0.24
 
 Stat. AD after spacings (mNP2-S)      :    0.96
 p-value of test no 33                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 35                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.23
 p-value of test no 36                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     277
 p-value of test no 37                 :    0.90
 
 Stat. AD (mNP2)                       :    0.26
 p-value of test no 38                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.91
 p-value of test no 40                 :    0.03
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.57
 p-value of test no 42                 :    0.68
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    1.41
 p-value of test no 44                 :    0.20
 
 Stat. AD after spacings (mNP2-S)      :    2.51
 p-value of test no 45                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.94
 p-value of test no 46                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.63
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   28.17
 p-value of test no 48                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.53
 p-value of test no 49                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.91
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.65
 p-value of test no 51                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.57
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.23
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.59
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.31
 p-value of test no 55                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1385.70
 p-value of test no 56                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7030.62
 p-value of test no 57                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 58                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
 p-value of test no 59                 :    0.9953
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 60                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.41
 p-value of test no 61                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 63                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 64                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   56.13
 p-value of test no 65                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    0.57
 p-value of test no 66                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.64
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.14
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907879
   j =  2                              :            46056
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45554
 p-value of test no 71                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869554
   j =  1                              :        399908895
   j =  2                              :            45548
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 73                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 76                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 77                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 79                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 81                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 83                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 85                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 86                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 87                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 88                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 92                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 95                 :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 97                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 98                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 99                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 102                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 104                :    0.79
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 106                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 107                :    0.17
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 108                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
 p-value of test no 109                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 110                :    0.38
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 111                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.52e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
 p-value of test no 113                :    0.38
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 114                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 115                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 117                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.29
 p-value of test no 118                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.54
 p-value of test no 119                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.04
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   40.93
 p-value of test no 121                :    0.9950
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.34
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.09
 p-value of test no 123                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.71
 p-value of test no 124                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   21.78
 p-value of test no 125                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 128                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.90
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 130                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 131                :    0.41
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 132                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.04
 p-value of test no 133                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.24
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.27
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.56
 p-value of test no 136                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.64
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 138                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.43
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.45
 p-value of test no 141                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 142                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 143                :    0.92
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17145.84
 p-value of test no 145                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.05
 p-value of test no 147                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.37
 p-value of test no 148                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.15
 p-value of test no 149                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   24.62
 p-value of test no 150                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.89
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   45.64
 p-value of test no 152                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   11.21
 p-value of test no 153                :    0.9919
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.17
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.41
 p-value of test no 155                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  139.60
 p-value of test no 156                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.10
 p-value of test no 157                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  519.38
 p-value of test no 158                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  156.02
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.86
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.65
 p-value of test no 161                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.18
 p-value of test no 162                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  478.27
 p-value of test no 163                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  154.36
 p-value of test no 164                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   90.23
 p-value of test no 165                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.92
 p-value of test no 166                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  336.20
 p-value of test no 167                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.58
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  392.55
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.80
 p-value of test no 170                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  360.78
 p-value of test no 171                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  430.37
 p-value of test no 172                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4883.98
 p-value of test no 173                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.40
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.64
 p-value of test no 175                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.92
 p-value of test no 176                :    0.71
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.89
 p-value of test no 178                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.19
 p-value of test no 179                :    0.58
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 180                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 181                :    0.92
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.54
 p-value of test no 183                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 184                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 185                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.022
 p-value of test no 188                :    0.49
 
 Sample variance                       :    0.40
 p-value of test no 189                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 195                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.58
 p-value of test no 196                :    0.38
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 197                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.59
 p-value of test no 198                :    0.23
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.66
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 202                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.20
 p-value of test no 203                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 205                :    0.96
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 206                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.27
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.58
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.064
 p-value of test no 213                :    0.89
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 214                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9860.62
 p-value of test no 215                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 216                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.14
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 220                :    0.57
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4886.89
 p-value of test no 222                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.36
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 225                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.01
 p-value of test no 226                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4134.10
 p-value of test no 227                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4175.41
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.54
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11759.66
 p-value of test no 230                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.59
 p-value of test no 231                :    0.20
 
 
 -----------------------------------------------
 Total number of bits:  8000023716
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.19
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  7999939713
 
 Normal statistic for number of bits   :   -0.48
 p-value of test no 234                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 236                :    0.75
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 240                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 241                :    0.07
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 242                :    0.06
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 243                :    0.03
 
 Sample variance                       :    1.19
 p-value of test no 244                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 247                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    0.99
 p-value of test no 249                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 250                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 252                :    0.93
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 253                :    0.59
 
 Sample variance                       :    0.95
 p-value of test no 254                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.14
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:01.52
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35961
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 4                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 5                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 6                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 7                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 8                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 10                 :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 11                 :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1477
 p-value of test no 12                 :  1.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334597
   j =  1                              :        599997046
   j =  2                              :             1477
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5314
 p-value of test no 13                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4354
 p-value of test no 14                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 15                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4428
 p-value of test no 16                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 17                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7406
 p-value of test no 19                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7374
 p-value of test no 21                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.35
 p-value of test no 22                 :    0.90
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 23                 :    0.52
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 27                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.65
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 29                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    1.06
 p-value of test no 30                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 32                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 33                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 34                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.21
 p-value of test no 35                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    2.60
 p-value of test no 36                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     338
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    1.43
 p-value of test no 39                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.31
 p-value of test no 41                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 42                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     154
 p-value of test no 43                 :    0.38
 
 Stat. AD (mNP2)                       :    0.97
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 45                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.15
 p-value of test no 46                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.29
 p-value of test no 47                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.12
 p-value of test no 48                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.00
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.61
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.57
 p-value of test no 51                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.36
 p-value of test no 52                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.91
 p-value of test no 53                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.76
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.76
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1405.22
 p-value of test no 56                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6981.58
 p-value of test no 57                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 59                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 60                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.63
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 64                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   49.56
 p-value of test no 65                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.07
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  116.23
 p-value of test no 67                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5076.26
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45722
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869722
   j =  1                              :        399908560
   j =  2                              :            45714
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46016
 p-value of test no 71                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870016
   j =  1                              :        399907970
   j =  2                              :            46012
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 72                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 76                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 77                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 80                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 81                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 83                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 84                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 86                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 91                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 92                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 95                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 99                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 101                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 102                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 103                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 105                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 107                :    0.65
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
 p-value of test no 109                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 111                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
 p-value of test no 112                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
 p-value of test no 113                :    0.15
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 114                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.37
 p-value of test no 115                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.62
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.15
 p-value of test no 117                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.97
 p-value of test no 118                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   46.70
 p-value of test no 119                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :  101.51
 p-value of test no 120                :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.43
 p-value of test no 121                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   19.56
 p-value of test no 122                :    0.9918
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.64
 p-value of test no 123                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.90
 p-value of test no 124                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   29.47
 p-value of test no 125                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 126                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 127                :    0.65
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.08
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.32
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 132                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.01
 p-value of test no 133                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.76
 p-value of test no 134                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.03
 p-value of test no 136                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.05
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 138                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.13
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 140                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  144.73
 p-value of test no 141                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 142                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.25
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17568.52
 p-value of test no 145                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.95
 p-value of test no 146                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.89
 p-value of test no 147                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.80
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.04
 p-value of test no 149                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.76
 p-value of test no 150                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.47
 p-value of test no 151                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.20
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.40
 p-value of test no 153                :    0.9954
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.94
 p-value of test no 154                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.80
 p-value of test no 155                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.80
 p-value of test no 156                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  179.29
 p-value of test no 157                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.41
 p-value of test no 158                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  119.23
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.54
 p-value of test no 160                :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.37
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.46
 p-value of test no 162                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.95
 p-value of test no 163                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.12
 p-value of test no 164                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.79
 p-value of test no 165                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.13
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.34
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4826.73
 p-value of test no 168                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.13
 p-value of test no 169                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.81
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  419.24
 p-value of test no 171                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  394.91
 p-value of test no 172                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4843.39
 p-value of test no 173                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.72
 p-value of test no 174                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  198.15
 p-value of test no 175                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.67
 p-value of test no 176                :    0.47
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.38
 p-value of test no 177                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.83
 p-value of test no 178                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.25
 p-value of test no 179                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 180                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.13
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 182                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.29
 p-value of test no 183                :    0.10
 
 Sample variance                       :    0.50
 p-value of test no 184                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.24
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.46
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.36
 p-value of test no 189                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
 p-value of test no 190                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 192                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 3.20e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.10
 p-value of test no 196                :    0.64
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.91
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.54
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  179.59
 p-value of test no 203                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 204                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 205                :    0.04
 
 Anderson-Darling statistic = A2       :    1.80
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  226.23
 p-value of test no 207                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 208                :    0.9998    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 209                :    0.04
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 210                :  9.4e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10431.44
 p-value of test no 211                :  1.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 213                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 214                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10132.37
 p-value of test no 215                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 216                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 217                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 219                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 221                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4803.87
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 223                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 225                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4809.81
 p-value of test no 226                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.27
 p-value of test no 227                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4237.61
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11881.59
 p-value of test no 229                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11752.38
 p-value of test no 230                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.29
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  7999990707
 
 Normal statistic for number of bits   :  -0.073
 p-value of test no 232                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.00
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  7999934484
 
 Normal statistic for number of bits   :   -0.52
 p-value of test no 234                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.70
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.40
 p-value of test no 239                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 242                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.29
 p-value of test no 243                :    0.61
 
 Sample variance                       :    1.13
 p-value of test no 244                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.59
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 247                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 248                :    0.56
 
 Sample variance                       :    1.10
 p-value of test no 249                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 250                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
 p-value of test no 251                :    0.9922
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 252                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.87
 p-value of test no 253                :    0.97
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.27
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:29.38
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35962
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 3                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 4                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 6                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 9                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 11                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4372
 p-value of test no 14                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 15                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4276
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4422
 p-value of test no 17                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7202
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7373
 p-value of test no 20                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7280
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.11
 p-value of test no 22                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 23                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.33
 p-value of test no 24                 :    0.91
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     923
 p-value of test no 25                 :    0.23
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    1.95
 p-value of test no 27                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 29                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.85
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     597
 p-value of test no 31                 :    0.54
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 32                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 33                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.12
 p-value of test no 34                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.13
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     325
 p-value of test no 37                 :    0.08
 
 Stat. AD (mNP2)                       :    0.76
 p-value of test no 38                 :    0.51
 
 Stat. AD after spacings (mNP2-S)      :    1.86
 p-value of test no 39                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 41                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 42                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 44                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    3.08
 p-value of test no 45                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.02
 p-value of test no 46                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.36
 p-value of test no 47                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.60
 p-value of test no 48                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.77
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.73
 p-value of test no 50                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.41
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.41
 p-value of test no 52                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.38
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  438.69
 p-value of test no 55                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1472.50
 p-value of test no 56                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7010.51
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 58                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 60                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.13
 p-value of test no 61                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 64                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.39
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:03:16.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.80
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  117.90
 p-value of test no 67                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5148.84
 p-value of test no 68                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45687
 p-value of test no 70                 :    0.81
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869687
   j =  1                              :        399908628
   j =  2                              :            45683
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46230
 p-value of test no 71                 :    0.05
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870230
   j =  1                              :        399907544
   j =  2                              :            46222
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 73                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 74                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 77                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 78                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 81                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 83                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 85                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 88                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.028
 p-value of test no 90                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 91                 :    0.15
 
 Anderson-Darling statistic = A2       :    1.51
 p-value of test no 92                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 93                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 95                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 97                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 98                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 99                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 101                :    0.59
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 104                :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 105                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 107                :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 108                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
 p-value of test no 109                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 110                :    0.50
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 111                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 113                :    0.51
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 114                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 115                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.36
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 117                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.047
 p-value of test no 118                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.92
 p-value of test no 119                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.50
 p-value of test no 120                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.99
 p-value of test no 121                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.33
 p-value of test no 122                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.89
 p-value of test no 123                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.37
 p-value of test no 124                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.21
 p-value of test no 125                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 126                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 127                :    0.79
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.32
 p-value of test no 129                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.23
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 132                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.81
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.74
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.33
 p-value of test no 135                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.79
 p-value of test no 137                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    3.02
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  156.52
 p-value of test no 141                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17293.34
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.51
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.81
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.14
 p-value of test no 148                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.92
 p-value of test no 150                :    0.9937
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.04
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.76
 p-value of test no 152                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.46
 p-value of test no 153                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.99
 p-value of test no 154                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.80
 p-value of test no 155                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.69
 p-value of test no 156                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.16
 p-value of test no 157                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.94
 p-value of test no 158                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  130.94
 p-value of test no 159                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.91
 p-value of test no 160                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.54
 p-value of test no 161                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  129.33
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  476.05
 p-value of test no 163                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.45
 p-value of test no 164                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.37
 p-value of test no 165                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.53
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.43
 p-value of test no 167                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5133.91
 p-value of test no 168                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  417.27
 p-value of test no 169                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  168.90
 p-value of test no 170                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.60
 p-value of test no 171                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.81
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4815.67
 p-value of test no 173                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  353.92
 p-value of test no 174                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  244.89
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.58
 p-value of test no 176                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.23
 p-value of test no 177                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.04
 p-value of test no 178                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.11
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 180                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 181                :    0.05
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 182                :    0.11
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.80
 p-value of test no 183                :    0.04
 
 Sample variance                       :    0.71
 p-value of test no 184                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 186                :    0.96
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 187                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.34
 p-value of test no 188                :    0.91
 
 Sample variance                       :    0.75
 p-value of test no 189                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
 p-value of test no 191                :    0.84
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 192                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 195                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   26.99
 p-value of test no 196                :  7.1e-4    *****
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.66
 p-value of test no 198                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 200                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 201                :    0.63
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.17
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 204                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 205                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 206                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  188.70
 p-value of test no 207                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.58
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 210                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.87
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 212                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10109.76
 p-value of test no 215                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.09
 p-value of test no 216                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.61
 p-value of test no 217                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 219                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 221                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4875.57
 p-value of test no 222                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 223                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 225                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.35
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.22
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.90
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11912.23
 p-value of test no 229                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11913.36
 p-value of test no 230                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.87
 p-value of test no 231                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999919595
 
 Normal statistic for number of bits   :   -0.64
 p-value of test no 232                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.30
 p-value of test no 233                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000038896
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.80
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 237                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.53
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 241                :    0.36
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 242                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 243                :    0.35
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.45
 p-value of test no 248                :    0.67
 
 Sample variance                       :    1.95
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 251                :    0.14
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 252                :    0.21
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 253                :    0.11
 
 Sample variance                       :    0.53
 p-value of test no 254                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:24.30
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  86  LongestHeadRun, r = 0           7.1e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35963
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1379
 p-value of test no 3                  :    0.35
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334499
   j =  1                              :        599997242
   j =  2                              :             1379
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 4                  :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 5                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 6                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 7                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1428
 p-value of test no 8                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334548
   j =  1                              :        599997144
   j =  2                              :             1428
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1399
 p-value of test no 9                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334519
   j =  1                              :        599997202
   j =  2                              :             1399
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 10                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 11                 :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1424
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334544
   j =  1                              :        599997152
   j =  2                              :             1424
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5274
 p-value of test no 13                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4410
 p-value of test no 14                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 15                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4330
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4464
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7278
 p-value of test no 18                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7393
 p-value of test no 19                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 20                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7422
 p-value of test no 21                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 22                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.42
 p-value of test no 23                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    1.04
 p-value of test no 24                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     935
 p-value of test no 25                 :    0.13
 
 Stat. AD (mNP2)                       :    0.78
 p-value of test no 26                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.53
 p-value of test no 27                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.25
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 29                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     625
 p-value of test no 31                 :    0.16
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 32                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.84
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 35                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 36                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     284
 p-value of test no 37                 :    0.81
 
 Stat. AD (mNP2)                       :    1.58
 p-value of test no 38                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    0.75
 p-value of test no 39                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.08
 p-value of test no 40                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.63
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.14
 p-value of test no 42                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 44                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.52
 p-value of test no 46                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.13
 p-value of test no 47                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.96
 p-value of test no 48                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.70
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.95
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   35.48
 p-value of test no 51                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.18
 p-value of test no 52                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 53                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.04
 p-value of test no 54                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  408.02
 p-value of test no 55                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1443.79
 p-value of test no 56                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7299.39
 p-value of test no 57                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   29.63
 p-value of test no 61                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.49
 p-value of test no 65                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.60
 p-value of test no 66                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.94
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5141.74
 p-value of test no 68                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 70                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908357
   j =  2                              :            45814
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45931
 p-value of test no 71                 :    0.41
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869931
   j =  1                              :        399908142
   j =  2                              :            45923
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 73                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 74                 :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.41
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 77                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 78                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 80                 :    0.15
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 81                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 84                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 85                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 86                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 88                 :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.53
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    : 1.87e-3
 p-value of test no 91                 :    0.9981
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 92                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 93                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 95                 :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 98                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 100                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 102                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 103                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 105                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 107                :    0.83
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 108                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
 p-value of test no 109                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
 p-value of test no 110                :    0.37
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 111                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
 p-value of test no 112                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.90
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 116                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.96
 p-value of test no 118                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.80
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.84
 p-value of test no 120                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.51
 p-value of test no 121                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.99
 p-value of test no 122                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.20
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.37
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.86
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 126                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.00
 p-value of test no 129                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.79
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.05
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.73
 p-value of test no 135                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 138                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 139                :    0.20
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 140                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  148.04
 p-value of test no 141                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 142                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 143                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17503.87
 p-value of test no 145                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   38.02
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.55
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.71
 p-value of test no 148                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 149                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.29
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.12
 p-value of test no 151                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.47
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   17.94
 p-value of test no 153                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.55
 p-value of test no 154                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.86
 p-value of test no 155                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.62
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  119.93
 p-value of test no 157                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.53
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.96
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.53
 p-value of test no 160                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.57
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.10
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  467.82
 p-value of test no 163                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  145.54
 p-value of test no 164                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.79
 p-value of test no 165                :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.76
 p-value of test no 166                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.10
 p-value of test no 167                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.69
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.39
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.30
 p-value of test no 170                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.48
 p-value of test no 171                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.09
 p-value of test no 172                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4942.98
 p-value of test no 173                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  355.28
 p-value of test no 174                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  193.48
 p-value of test no 175                :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.10
 p-value of test no 176                :    0.69
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.21
 p-value of test no 177                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   23.56
 p-value of test no 178                :    0.02
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.23
 p-value of test no 179                :    0.01
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 181                :    0.95
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 183                :    0.94
 
 Sample variance                       :    1.05
 p-value of test no 184                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    4.16
 p-value of test no 187                :  7.6e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.13
 p-value of test no 188                :    0.02
 
 Sample variance                       :    2.46
 p-value of test no 189                :  8.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 190                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
 p-value of test no 191                :    0.72
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 192                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
 p-value of test no 193                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
 p-value of test no 194                :    0.69
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 195                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.17
 p-value of test no 196                :    0.98
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.67
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 200                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 202                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.64
 p-value of test no 203                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 204                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.54
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.77
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 208                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9849.77
 p-value of test no 211                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.73
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 214                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9899.47
 p-value of test no 215                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.22
 p-value of test no 216                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.30
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.14
 p-value of test no 218                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 219                :  8.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4785.73
 p-value of test no 222                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4793.43
 p-value of test no 226                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.36
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4110.28
 p-value of test no 228                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11985.62
 p-value of test no 229                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11904.97
 p-value of test no 230                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.87
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  7999960617
 
 Normal statistic for number of bits   :   -0.31
 p-value of test no 232                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   42.34
 p-value of test no 233                :    0.87
 
 
 -----------------------------------------------
 Total number of bits:  7999927548
 
 Normal statistic for number of bits   :   -0.57
 p-value of test no 234                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    3.97
 p-value of test no 237                :  9.4e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.65
 p-value of test no 238                :    0.9959
 
 Sample variance                       :    0.59
 p-value of test no 239                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 241                :    0.79
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 242                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 243                :    0.67
 
 Sample variance                       :    1.01
 p-value of test no 244                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 247                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 248                :    0.72
 
 Sample variance                       :    1.14
 p-value of test no 249                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 251                :    0.90
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 252                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.10
 p-value of test no 253                :    0.86
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.09
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:25.18
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35964
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 4                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 5                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 7                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 8                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1237
 p-value of test no 9                  :    0.9998    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334357
   j =  1                              :        599997526
   j =  2                              :             1237
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 10                 :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5488
 p-value of test no 13                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4194
 p-value of test no 14                 :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7332
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4236
 p-value of test no 16                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4377
 p-value of test no 17                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7360
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7211
 p-value of test no 19                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 20                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 21                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.89
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.19
 p-value of test no 23                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 24                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     862
 p-value of test no 25                 :    0.89
 
 Stat. AD (mNP2)                       :    0.90
 p-value of test no 26                 :    0.42
 
 Stat. AD after spacings (mNP2-S)      :    1.07
 p-value of test no 27                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.10
 p-value of test no 28                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 29                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    1.07
 p-value of test no 30                 :    0.32
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     580
 p-value of test no 31                 :    0.79
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 33                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.59
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.85
 p-value of test no 35                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.41
 p-value of test no 36                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 39                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 40                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 41                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 42                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     153
 p-value of test no 43                 :    0.41
 
 Stat. AD (mNP2)                       :    0.91
 p-value of test no 44                 :    0.41
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 45                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.44
 p-value of test no 46                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   16.18
 p-value of test no 47                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.48
 p-value of test no 48                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.96
 p-value of test no 49                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.74
 p-value of test no 50                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.34
 p-value of test no 51                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.17
 p-value of test no 52                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   33.65
 p-value of test no 53                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  229.31
 p-value of test no 54                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  441.80
 p-value of test no 55                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1438.91
 p-value of test no 56                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7246.64
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 60                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.90
 p-value of test no 61                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.21
 p-value of test no 65                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.21
 p-value of test no 66                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  129.57
 p-value of test no 67                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5078.34
 p-value of test no 68                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45896
 p-value of test no 70                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869896
   j =  1                              :        399908209
   j =  2                              :            45894
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 71                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908695
   j =  2                              :            45639
   j =  3                              :                9
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 74                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 77                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 78                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 80                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 81                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.92
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 83                 :  6.8e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 84                 :    0.93
 
 Anderson-Darling statistic = A2       :    2.91
 p-value of test no 85                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 87                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 88                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 92                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 95                 :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 97                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.036
 p-value of test no 98                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.034
 p-value of test no 100                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 101                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 102                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 103                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.40
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 108                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
 p-value of test no 109                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
 p-value of test no 110                :    0.26
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 111                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
 p-value of test no 112                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 114                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 116                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.64
 p-value of test no 117                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 118                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.24
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.12
 p-value of test no 120                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.56
 p-value of test no 121                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.43
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.76
 p-value of test no 123                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.53
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   25.53
 p-value of test no 125                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.058
 p-value of test no 126                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 127                :    0.14
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 128                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.05
 p-value of test no 129                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 130                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 131                :    0.69
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 132                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   38.41
 p-value of test no 133                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.54
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.77
 p-value of test no 135                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.93
 p-value of test no 136                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.85
 p-value of test no 137                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 138                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.32
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 140                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.77
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 143                :    0.95
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 144                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17126.27
 p-value of test no 145                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.63
 p-value of test no 146                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.98
 p-value of test no 147                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.34
 p-value of test no 148                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.97
 p-value of test no 149                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.83
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.57
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   48.21
 p-value of test no 152                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.06
 p-value of test no 153                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   32.34
 p-value of test no 154                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.07
 p-value of test no 155                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.66
 p-value of test no 156                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.55
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.47
 p-value of test no 158                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.47
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.43
 p-value of test no 160                :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.20
 p-value of test no 161                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.75
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.58
 p-value of test no 163                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.31
 p-value of test no 164                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.61
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.03
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  352.10
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5126.36
 p-value of test no 168                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  414.41
 p-value of test no 169                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  163.99
 p-value of test no 170                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.86
 p-value of test no 171                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.18
 p-value of test no 172                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5159.10
 p-value of test no 173                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  386.55
 p-value of test no 174                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.18
 p-value of test no 175                :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.99
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.63
 p-value of test no 177                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.77
 p-value of test no 178                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.16
 p-value of test no 179                :    0.56
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 181                :    0.24
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 182                :    0.28
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.22
 p-value of test no 183                :    0.11
 
 Sample variance                       :    1.11
 p-value of test no 184                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.40
 p-value of test no 188                :    0.35
 
 Sample variance                       :    0.50
 p-value of test no 189                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
 p-value of test no 190                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
 p-value of test no 193                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.65
 p-value of test no 196                :    0.47
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.20
 p-value of test no 198                :    0.84
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 200                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 201                :    0.57
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 202                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.40
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 205                :    0.02
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 206                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.25
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 208                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 210                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10035.72
 p-value of test no 211                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 213                :    0.11
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 214                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.78
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 216                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 217                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.00
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 1.21e-3
 p-value of test no 220                :    0.9988
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 221                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4679.99
 p-value of test no 222                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 223                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 225                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4925.25
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.41
 p-value of test no 227                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4027.04
 p-value of test no 228                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11657.18
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.56
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.58
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000071440
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 232                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.61
 p-value of test no 233                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  8000017599
 
 Normal statistic for number of bits   :    0.14
 p-value of test no 234                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 235                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.45
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 237                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.55
 p-value of test no 238                :    0.71
 
 Sample variance                       :    1.52
 p-value of test no 239                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 242                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.049
 p-value of test no 243                :    0.48
 
 Sample variance                       :    1.66
 p-value of test no 244                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 246                :    0.08
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 247                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.26
 p-value of test no 248                :    0.10
 
 Sample variance                       :    1.15
 p-value of test no 249                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 250                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 251                :    0.73
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 253                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:06.45
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           0.9998 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35965
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 4                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1347
 p-value of test no 5                  :    0.67
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334467
   j =  1                              :        599997306
   j =  2                              :             1347
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 7                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 8                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 9                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 10                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 11                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 12                 :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5300
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4222
 p-value of test no 14                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7252
 p-value of test no 15                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4300
 p-value of test no 16                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 18                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7390
 p-value of test no 20                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7212
 p-value of test no 21                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    3.13
 p-value of test no 24                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     999
 p-value of test no 25                 :  6.2e-4    *****
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    3.15
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 30                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    1.15
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.29
 p-value of test no 35                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 36                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    3.33
 p-value of test no 38                 :    0.02
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 39                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 41                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.88
 p-value of test no 44                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.98
 p-value of test no 46                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.60
 p-value of test no 47                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   32.78
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.39
 p-value of test no 49                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.31
 p-value of test no 50                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.60
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.19
 p-value of test no 52                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.25
 p-value of test no 53                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  206.98
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  523.61
 p-value of test no 55                 :  2.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1420.06
 p-value of test no 56                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7128.23
 p-value of test no 57                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 58                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.04
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   57.16
 p-value of test no 65                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:14.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.36
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  138.47
 p-value of test no 67                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5115.22
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45735
 p-value of test no 70                 :    0.75
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869735
   j =  1                              :        399908533
   j =  2                              :            45729
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45515
 p-value of test no 71                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869515
   j =  1                              :        399908971
   j =  2                              :            45513
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 74                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.51
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 76                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 77                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 81                 :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 84                 :    0.98
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 85                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 86                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 87                 :    0.51
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 88                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 90                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 92                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 93                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 97                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 101                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 104                :    0.48
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 106                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 108                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.61e-6
 p-value of test no 109                :    0.9982
 
 Kolmogorov-Smirnov- statistic = D-    : 3.47e-4
 p-value of test no 110                :  8.1e-3
 
 Anderson-Darling statistic = A2       :    3.59
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
 p-value of test no 112                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
 p-value of test no 113                :    0.14
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.52
 p-value of test no 115                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.072
 p-value of test no 116                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 117                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.32
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.58
 p-value of test no 119                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.74
 p-value of test no 120                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.44
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.80
 p-value of test no 122                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.64
 p-value of test no 123                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.69
 p-value of test no 124                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   24.02
 p-value of test no 125                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 126                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.38
 p-value of test no 129                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 132                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.53
 p-value of test no 133                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    9.40
 p-value of test no 134                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.67
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.17
 p-value of test no 136                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.95
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 139                :    0.72
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  118.15
 p-value of test no 141                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.032
 p-value of test no 143                :    0.96
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 144                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17153.09
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.79
 p-value of test no 146                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.27
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.90
 p-value of test no 148                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :    9.24
 p-value of test no 149                :    0.9970
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.04
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   23.72
 p-value of test no 151                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   18.68
 p-value of test no 152                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.44
 p-value of test no 153                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.74
 p-value of test no 154                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.71
 p-value of test no 155                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.22
 p-value of test no 156                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.62
 p-value of test no 157                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.63
 p-value of test no 158                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.00
 p-value of test no 159                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.48
 p-value of test no 160                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  117.01
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.64
 p-value of test no 162                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.09
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  162.59
 p-value of test no 164                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.83
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.97
 p-value of test no 166                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.34
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.74
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  363.38
 p-value of test no 169                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  202.49
 p-value of test no 170                :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.93
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.67
 p-value of test no 172                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5274.45
 p-value of test no 173                :  3.4e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  345.51
 p-value of test no 174                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.47
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.35
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.69
 p-value of test no 178                :    0.73
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.39
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.37
 p-value of test no 183                :    0.64
 
 Sample variance                       :    0.43
 p-value of test no 184                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 188                :    0.38
 
 Sample variance                       :    0.80
 p-value of test no 189                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
 p-value of test no 191                :    0.73
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 192                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.22
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 195                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.31
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.06
 p-value of test no 198                :    0.53
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.69
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 202                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.58
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 204                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 205                :    0.77
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 206                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.59
 p-value of test no 207                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.61
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 210                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.17
 p-value of test no 211                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 212                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 213                :    0.38
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.48
 p-value of test no 215                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.30
 p-value of test no 216                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 217                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.92
 p-value of test no 218                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 219                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 220                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4827.09
 p-value of test no 222                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 224                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 225                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4892.22
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.10
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4073.31
 p-value of test no 228                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11648.54
 p-value of test no 229                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12076.99
 p-value of test no 230                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.85
 p-value of test no 231                :    0.37
 
 
 -----------------------------------------------
 Total number of bits:  8000114703
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.19
 p-value of test no 233                :    0.39
 
 
 -----------------------------------------------
 Total number of bits:  7999966701
 
 Normal statistic for number of bits   :   -0.26
 p-value of test no 234                :    0.60
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 235                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 236                :    0.81
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 237                :    0.34
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.97
 p-value of test no 238                :    0.83
 
 Sample variance                       :    0.51
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 241                :    0.08
 
 Anderson-Darling statistic = A2       :    1.98
 p-value of test no 242                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.75
 p-value of test no 243                :    0.04
 
 Sample variance                       :    1.49
 p-value of test no 244                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 245                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 246                :    0.71
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.23
 p-value of test no 248                :    0.89
 
 Sample variance                       :    1.96
 p-value of test no 249                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 250                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 251                :    0.84
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 252                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    0.63
 p-value of test no 254                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:41.40
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  22  ClosePairs NJumps, t = 3        6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35966
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 3                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 4                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 6                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 7                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 8                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 9                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 10                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1261
 p-value of test no 11                 :    0.9975
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334381
   j =  1                              :        599997478
   j =  2                              :             1261
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4406
 p-value of test no 14                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 18                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7196
 p-value of test no 19                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7453
 p-value of test no 20                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.92
 p-value of test no 23                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    1.05
 p-value of test no 24                 :    0.33
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     924
 p-value of test no 25                 :    0.22
 
 Stat. AD (mNP2)                       :    0.67
 p-value of test no 26                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    1.21
 p-value of test no 27                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.82
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 30                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     596
 p-value of test no 31                 :    0.55
 
 Stat. AD (mNP2)                       :    0.13
 p-value of test no 32                 :    0.9996    *****
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 33                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.60
 p-value of test no 34                 :    0.65
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.60
 p-value of test no 35                 :    0.64
 
 Test on the Nm values of W_{n,i}(mNP1):    1.71
 p-value of test no 36                 :    0.13
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     335
 p-value of test no 37                 :    0.02
 
 Stat. AD (mNP2)                       :    0.32
 p-value of test no 38                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.95
 p-value of test no 40                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.35
 p-value of test no 41                 :    0.06
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    3.31
 p-value of test no 45                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.90
 p-value of test no 46                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.75
 p-value of test no 47                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.97
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.22
 p-value of test no 49                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.88
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.98
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.05
 p-value of test no 52                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.53
 p-value of test no 53                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.13
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  476.20
 p-value of test no 55                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1413.54
 p-value of test no 56                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7207.63
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 58                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   26.32
 p-value of test no 61                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 62                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 63                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 64                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   43.60
 p-value of test no 65                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.50
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   98.37
 p-value of test no 67                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4874.46
 p-value of test no 68                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45995
 p-value of test no 70                 :    0.30
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869995
   j =  1                              :        399908014
   j =  2                              :            45987
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45913
 p-value of test no 71                 :    0.44
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869913
   j =  1                              :        399908177
   j =  2                              :            45907
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 72                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 73                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 74                 :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.70
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 77                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 78                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 79                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
 p-value of test no 80                 :    0.9982
 
 Anderson-Darling statistic = A2       :    2.30
 p-value of test no 81                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 83                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 87                 :    0.61
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 88                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 90                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 91                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.17
 p-value of test no 92                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 93                 :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 95                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.81
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 98                 :    0.03
 
 Anderson-Darling statistic = A2       :    3.73
 p-value of test no 99                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 100                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 101                :    0.20
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 102                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 103                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 104                :    0.75
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 105                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.52
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
 p-value of test no 110                :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 111                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
 p-value of test no 113                :    0.81
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 114                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.14
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 116                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.24
 p-value of test no 117                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.99
 p-value of test no 118                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   29.56
 p-value of test no 119                : 1 -  2.0e-5    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   57.48
 p-value of test no 120                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.58
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.29
 p-value of test no 122                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.97
 p-value of test no 123                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.75
 p-value of test no 124                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.17
 p-value of test no 125                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 126                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 127                :    0.07
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 128                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   50.63
 p-value of test no 129                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 130                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 131                :    0.77
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.87
 p-value of test no 133                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.03
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.89
 p-value of test no 135                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.09
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.99
 p-value of test no 137                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 138                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.42
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 140                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  146.95
 p-value of test no 141                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 143                :    0.41
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 144                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17486.74
 p-value of test no 145                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.58
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   47.96
 p-value of test no 147                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.99
 p-value of test no 148                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.07
 p-value of test no 149                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   25.66
 p-value of test no 150                :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.84
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.25
 p-value of test no 152                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.99
 p-value of test no 153                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.17
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.10
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.16
 p-value of test no 156                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.74
 p-value of test no 157                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.88
 p-value of test no 158                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.14
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   52.68
 p-value of test no 160                :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  142.10
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.71
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.74
 p-value of test no 163                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.86
 p-value of test no 164                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.01
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.29
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.14
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5215.53
 p-value of test no 168                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  340.42
 p-value of test no 169                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.34
 p-value of test no 170                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.41
 p-value of test no 171                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.69
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4948.08
 p-value of test no 173                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  420.65
 p-value of test no 174                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.14
 p-value of test no 175                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.26
 p-value of test no 176                :    0.76
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.09
 p-value of test no 178                :    0.85
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.012
 p-value of test no 179                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.31
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 182                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.61
 p-value of test no 183                :    0.27
 
 Sample variance                       :    1.15
 p-value of test no 184                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 186                :    0.95
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 187                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 188                :    0.84
 
 Sample variance                       :    1.20
 p-value of test no 189                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
 p-value of test no 190                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 192                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
 p-value of test no 193                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
 p-value of test no 194                :    0.61
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 195                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.77
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.65
 p-value of test no 198                :    0.17
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 200                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 1.52e-3
 p-value of test no 201                :    0.9985
 
 Anderson-Darling statistic = A2       :    4.27
 p-value of test no 202                :  6.8e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.21
 p-value of test no 203                :    0.9971
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 204                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.69
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 206                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.38
 p-value of test no 207                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.68
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10001.97
 p-value of test no 211                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.035
 p-value of test no 213                :    0.95
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9820.90
 p-value of test no 215                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 217                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 218                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 219                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.41
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4972.79
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 223                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
 p-value of test no 224                :    0.9933
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 225                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4722.49
 p-value of test no 226                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4145.44
 p-value of test no 227                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4201.79
 p-value of test no 228                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11909.13
 p-value of test no 229                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12034.81
 p-value of test no 230                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.41
 p-value of test no 231                :    0.72
 
 
 -----------------------------------------------
 Total number of bits:  7999950564
 
 Normal statistic for number of bits   :   -0.39
 p-value of test no 232                :    0.65
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.40
 p-value of test no 233                :    0.42
 
 
 -----------------------------------------------
 Total number of bits:  8000071239
 
 Normal statistic for number of bits   :    0.56
 p-value of test no 234                :    0.29
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.54
 p-value of test no 237                :    0.17
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.67
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 242                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.63
 p-value of test no 243                :    0.05
 
 Sample variance                       :    1.53
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 245                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.66
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
 p-value of test no 250                :    0.9958
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 251                :    0.03
 
 Anderson-Darling statistic = A2       :    3.74
 p-value of test no 252                :    0.01
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.78
 p-value of test no 253                :  2.7e-3
 
 Sample variance                       :    1.01
 p-value of test no 254                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:43.02
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  23  ClosePairs mNP2, t = 5          0.9996 
  59  WeightDistrib, r = 0           1 -  2.0e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35967
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 3                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1312
 p-value of test no 4                  :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334432
   j =  1                              :        599997376
   j =  2                              :             1312
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 5                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 7                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 8                  :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 9                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 10                 :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5449
 p-value of test no 13                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4362
 p-value of test no 14                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4469
 p-value of test no 16                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4373
 p-value of test no 17                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7309
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 19                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 21                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.36
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 23                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    1.82
 p-value of test no 24                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 28                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.58
 p-value of test no 29                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 30                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    1.30
 p-value of test no 32                 :    0.23
 
 Stat. AD after spacings (mNP2-S)      :    1.44
 p-value of test no 33                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.22
 p-value of test no 34                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.02
 p-value of test no 35                 :    0.34
 
 Test on the Nm values of W_{n,i}(mNP1):    1.65
 p-value of test no 36                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 38                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    2.19
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.60
 p-value of test no 40                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.41
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 42                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     150
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    2.14
 p-value of test no 44                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.33
 p-value of test no 45                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.61
 p-value of test no 46                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.55
 p-value of test no 47                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.02
 p-value of test no 48                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.01
 p-value of test no 49                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.39
 p-value of test no 50                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.22
 p-value of test no 51                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   34.46
 p-value of test no 52                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.19
 p-value of test no 53                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  265.21
 p-value of test no 54                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  435.90
 p-value of test no 55                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1416.92
 p-value of test no 56                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.06
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 59                 :    0.95
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 60                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   21.80
 p-value of test no 61                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 63                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 64                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.27
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.11
 p-value of test no 66                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.89
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4839.21
 p-value of test no 68                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45986
 p-value of test no 70                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869986
   j =  1                              :        399908030
   j =  2                              :            45982
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46061
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870061
   j =  1                              :        399907885
   j =  2                              :            46047
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 72                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 73                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 77                 :    0.41
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 78                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 81                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 85                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 87                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 88                 :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 91                 :    0.64
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 92                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 94                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 95                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 97                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 98                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 99                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 100                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.26
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.43
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 107                :    0.87
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
 p-value of test no 109                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
 p-value of test no 110                :    0.78
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 111                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 5.69e-5
 p-value of test no 113                :    0.88
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.13
 p-value of test no 115                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 116                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.43
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 118                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.11
 p-value of test no 119                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.57
 p-value of test no 120                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.55
 p-value of test no 121                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.74
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.33
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.23
 p-value of test no 124                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   35.67
 p-value of test no 125                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 128                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.46
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.61
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 132                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.26
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.06
 p-value of test no 134                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.50
 p-value of test no 135                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.59
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 138                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 139                :    0.15
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 140                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.18
 p-value of test no 141                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 142                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 143                :    0.75
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17226.00
 p-value of test no 145                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   43.23
 p-value of test no 146                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.62
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.98
 p-value of test no 148                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.80
 p-value of test no 150                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.83
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.71
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.27
 p-value of test no 153                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.86
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.69
 p-value of test no 155                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.93
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.15
 p-value of test no 157                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  606.01
 p-value of test no 158                :  7.8e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  171.52
 p-value of test no 159                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.34
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.80
 p-value of test no 161                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  189.62
 p-value of test no 162                :  8.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.20
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  113.35
 p-value of test no 164                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.83
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  421.87
 p-value of test no 166                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.74
 p-value of test no 167                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5000.77
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  406.00
 p-value of test no 169                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  176.10
 p-value of test no 170                :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.20
 p-value of test no 171                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.63
 p-value of test no 172                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5040.45
 p-value of test no 173                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.03
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  216.69
 p-value of test no 175                :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.52
 p-value of test no 176                :    0.66
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.80
 p-value of test no 177                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.31
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.53
 p-value of test no 179                :    0.70
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 180                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 181                :    0.91
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 182                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 183                :    0.80
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 186                :    0.93
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 187                :    0.14
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.90
 p-value of test no 189                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 192                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 193                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
 p-value of test no 194                :    0.93
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.53
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.68
 p-value of test no 198                :    0.88
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 200                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 201                :    0.91
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 202                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  175.67
 p-value of test no 203                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 204                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 206                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  173.27
 p-value of test no 207                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 210                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9887.31
 p-value of test no 211                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 212                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 213                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9895.49
 p-value of test no 215                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.23
 p-value of test no 216                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.32
 p-value of test no 217                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.79
 p-value of test no 218                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4805.83
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.65
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 225                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4910.38
 p-value of test no 226                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4026.63
 p-value of test no 227                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4216.83
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11455.48
 p-value of test no 229                :    0.9923
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12160.09
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.18
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000098089
 
 Normal statistic for number of bits   :    0.78
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.04
 p-value of test no 233                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000023245
 
 Normal statistic for number of bits   :    0.18
 p-value of test no 234                :    0.43
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 235                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 236                :    0.16
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 238                :    0.05
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 241                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 242                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 243                :    0.43
 
 Sample variance                       :    1.16
 p-value of test no 244                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 246                :    0.91
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 247                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.99
 p-value of test no 248                :    0.84
 
 Sample variance                       :    0.80
 p-value of test no 249                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 252                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.86
 p-value of test no 253                :    0.80
 
 Sample variance                       :    0.84
 p-value of test no 254                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:19.04
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 J (L=1000, r=0)     7.8e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35968
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 3                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 4                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 5                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 7                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 8                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1498
 p-value of test no 9                  :  1.9e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334618
   j =  1                              :        599997004
   j =  2                              :             1498
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 10                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5429
 p-value of test no 13                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4443
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7330
 p-value of test no 15                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4343
 p-value of test no 16                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4375
 p-value of test no 17                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7239
 p-value of test no 18                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7372
 p-value of test no 19                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 21                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.81
 p-value of test no 22                 :    0.47
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.00
 p-value of test no 23                 :    0.09
 
 Test on the Nm values of W_{n,i}(mNP1):    0.89
 p-value of test no 24                 :    0.42
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     946
 p-value of test no 25                 :    0.07
 
 Stat. AD (mNP2)                       :    0.55
 p-value of test no 26                 :    0.69
 
 Stat. AD after spacings (mNP2-S)      :    1.80
 p-value of test no 27                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 28                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.14
 p-value of test no 29                 :    0.9989
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 30                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     635
 p-value of test no 31                 :    0.08
 
 Stat. AD (mNP2)                       :    0.70
 p-value of test no 32                 :    0.56
 
 Stat. AD after spacings (mNP2-S)      :    2.73
 p-value of test no 33                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.78
 p-value of test no 34                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 35                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    2.41
 p-value of test no 36                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    0.36
 p-value of test no 38                 :    0.89
 
 Stat. AD after spacings (mNP2-S)      :    2.02
 p-value of test no 39                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.74
 p-value of test no 40                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    1.62
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 45                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.25
 p-value of test no 46                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.26
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   19.57
 p-value of test no 48                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.72
 p-value of test no 49                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.77
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.30
 p-value of test no 52                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.06
 p-value of test no 53                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  237.81
 p-value of test no 54                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.92
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1400.20
 p-value of test no 56                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6770.20
 p-value of test no 57                 :    0.9906
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 58                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.55
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.93
 p-value of test no 60                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   46.61
 p-value of test no 61                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.79
 p-value of test no 65                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.40
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  144.63
 p-value of test no 67                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.67
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45640
 p-value of test no 70                 :    0.87
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869640
   j =  1                              :        399908725
   j =  2                              :            45630
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46064
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870064
   j =  1                              :        399907877
   j =  2                              :            46054
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 73                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.40
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 78                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 79                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 80                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 83                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.033
 p-value of test no 86                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 88                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 91                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 92                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 93                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.58
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 95                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.75
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 97                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 99                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 100                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.11
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 102                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 106                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 107                :    0.81
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 108                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
 p-value of test no 109                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
 p-value of test no 110                :    0.29
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
 p-value of test no 113                :    0.49
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 114                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 115                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 116                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.018
 p-value of test no 117                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.014
 p-value of test no 118                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.16
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   91.66
 p-value of test no 120                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.80
 p-value of test no 121                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.77
 p-value of test no 122                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.80
 p-value of test no 123                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.27
 p-value of test no 124                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   32.95
 p-value of test no 125                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 127                :    0.68
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.01
 p-value of test no 129                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 130                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 131                :    0.34
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.18
 p-value of test no 133                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 134                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.82
 p-value of test no 135                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 136                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.72
 p-value of test no 137                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 138                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.34
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 140                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  138.94
 p-value of test no 141                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 144                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17293.71
 p-value of test no 145                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.18
 p-value of test no 146                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.68
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.37
 p-value of test no 148                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.65
 p-value of test no 149                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.57
 p-value of test no 150                :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   17.58
 p-value of test no 151                :    0.9958
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.39
 p-value of test no 152                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.47
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.49
 p-value of test no 154                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.73
 p-value of test no 155                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.16
 p-value of test no 156                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.61
 p-value of test no 157                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  400.69
 p-value of test no 158                :    0.9996    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  110.92
 p-value of test no 159                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.09
 p-value of test no 160                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.16
 p-value of test no 161                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.80
 p-value of test no 162                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  468.35
 p-value of test no 163                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.51
 p-value of test no 164                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   61.03
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.11
 p-value of test no 166                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.18
 p-value of test no 167                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4873.00
 p-value of test no 168                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  403.83
 p-value of test no 169                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  252.54
 p-value of test no 170                :  7.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  408.52
 p-value of test no 171                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.68
 p-value of test no 172                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5011.97
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  389.83
 p-value of test no 174                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.77
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.77
 p-value of test no 176                :    0.46
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.26
 p-value of test no 177                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.95
 p-value of test no 178                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.61
 p-value of test no 179                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
 p-value of test no 181                :    0.99
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 182                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.74
 p-value of test no 183                :    0.96
 
 Sample variance                       :    1.06
 p-value of test no 184                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 186                :    0.14
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 187                :    0.16
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.27
 p-value of test no 188                :    0.10
 
 Sample variance                       :    1.89
 p-value of test no 189                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
 p-value of test no 193                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
 p-value of test no 194                :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 195                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.80
 p-value of test no 196                :    0.56
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.32
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 200                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 202                :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.23
 p-value of test no 203                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 204                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.58
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 206                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.50
 p-value of test no 207                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 208                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 209                :    0.98
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 210                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9784.74
 p-value of test no 211                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 212                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 214                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10182.17
 p-value of test no 215                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.57
 p-value of test no 216                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 217                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 218                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    2.42
 p-value of test no 221                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.32
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 225                :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4798.62
 p-value of test no 226                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4337.93
 p-value of test no 227                :  8.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4233.35
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11658.60
 p-value of test no 229                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11874.45
 p-value of test no 230                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.71
 p-value of test no 231                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000034612
 
 Normal statistic for number of bits   :    0.27
 p-value of test no 232                :    0.39
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.36
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999875450
 
 Normal statistic for number of bits   :   -0.98
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 237                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.69
 p-value of test no 238                :    0.24
 
 Sample variance                       :    1.06
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 242                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 243                :    0.70
 
 Sample variance                       :    0.81
 p-value of test no 244                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 245                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.15
 
 Anderson-Darling statistic = A2       :    1.93
 p-value of test no 247                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.88
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 250                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.50
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 252                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 253                :    0.35
 
 Sample variance                       :    0.68
 p-value of test no 254                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.65
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:12.13
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   9  CollisionOver, t = 14           1.9e-4
  76  RandomWalk1 J (L=1000, r=0)     0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35969
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 3                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 4                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1440
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334560
   j =  1                              :        599997120
   j =  2                              :             1440
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 6                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 7                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 8                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997147
   j =  2                              :             1425
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 9                  :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 10                 :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 11                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1423
 p-value of test no 12                 :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334543
   j =  1                              :        599997154
   j =  2                              :             1423
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5286
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 14                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 15                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4381
 p-value of test no 16                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4235
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7325
 p-value of test no 18                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7294
 p-value of test no 19                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7246
 p-value of test no 20                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7307
 p-value of test no 21                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 22                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 23                 :    0.72
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     948
 p-value of test no 25                 :    0.06
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 26                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 27                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 29                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.93
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     551
 p-value of test no 31                 :    0.98
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    2.57
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.63
 p-value of test no 34                 :    0.62
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.93
 p-value of test no 36                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     306
 p-value of test no 37                 :    0.37
 
 Stat. AD (mNP2)                       :    1.02
 p-value of test no 38                 :    0.35
 
 Stat. AD after spacings (mNP2-S)      :    1.24
 p-value of test no 39                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.79
 p-value of test no 40                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 41                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.48
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.09
 p-value of test no 44                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.79
 p-value of test no 45                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.92
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.08
 p-value of test no 47                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   24.57
 p-value of test no 48                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.05
 p-value of test no 49                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.69
 p-value of test no 50                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.86
 p-value of test no 51                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.56
 p-value of test no 52                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.61
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.48
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  400.73
 p-value of test no 55                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1446.33
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6887.99
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 59                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.16
 p-value of test no 60                 :    0.28
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.83
 p-value of test no 61                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 62                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.34
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.05
 p-value of test no 66                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.05
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5105.66
 p-value of test no 68                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46062
 p-value of test no 70                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870062
   j =  1                              :        399907881
   j =  2                              :            46052
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45988
 p-value of test no 71                 :    0.31
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869988
   j =  1                              :        399908026
   j =  2                              :            45984
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 72                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 76                 :  3.9e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    4.00
 p-value of test no 78                 :  8.8e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 80                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 81                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 83                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 90                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 98                 :    0.84
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 99                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 101                :    0.98
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 104                :    0.09
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 105                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 108                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
 p-value of test no 109                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.95e-5
 p-value of test no 112                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 113                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 114                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.19
 p-value of test no 115                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.34
 p-value of test no 116                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 117                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.20
 p-value of test no 118                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.88
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   77.88
 p-value of test no 120                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.21
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.14
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   51.50
 p-value of test no 123                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   49.68
 p-value of test no 124                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   39.15
 p-value of test no 125                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 128                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   60.73
 p-value of test no 129                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 130                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 131                :    0.08
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   47.30
 p-value of test no 133                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.74
 p-value of test no 134                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.65
 p-value of test no 135                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.66
 p-value of test no 136                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 138                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 139                :    0.08
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  147.85
 p-value of test no 141                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 142                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 143                :    0.90
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17246.04
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.94
 p-value of test no 146                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.59
 p-value of test no 147                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.65
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.78
 p-value of test no 149                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.88
 p-value of test no 150                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.11
 p-value of test no 151                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.37
 p-value of test no 152                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.48
 p-value of test no 153                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.13
 p-value of test no 154                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   26.08
 p-value of test no 155                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.96
 p-value of test no 156                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.22
 p-value of test no 157                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  560.69
 p-value of test no 158                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.74
 p-value of test no 159                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.23
 p-value of test no 160                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.35
 p-value of test no 161                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.33
 p-value of test no 162                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.09
 p-value of test no 163                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.80
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   82.86
 p-value of test no 165                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  423.20
 p-value of test no 166                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.86
 p-value of test no 167                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.92
 p-value of test no 168                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  409.27
 p-value of test no 169                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  149.44
 p-value of test no 170                :    0.9970
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.83
 p-value of test no 171                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.01
 p-value of test no 172                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5116.61
 p-value of test no 173                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  361.41
 p-value of test no 174                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.03
 p-value of test no 175                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.40
 p-value of test no 176                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    2.01
 p-value of test no 177                :    0.02
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.21
 p-value of test no 178                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 180                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 181                :    0.62
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.30
 p-value of test no 183                :    0.62
 
 Sample variance                       :    0.44
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.39
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 187                :    0.82
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    0.70
 p-value of test no 189                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.41e-3
 p-value of test no 190                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
 p-value of test no 193                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.24
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.14
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.62
 p-value of test no 198                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 202                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  203.77
 p-value of test no 203                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 205                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 206                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  208.82
 p-value of test no 207                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 208                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.031
 p-value of test no 209                :    0.96
 
 Anderson-Darling statistic = A2       :    1.87
 p-value of test no 210                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9752.06
 p-value of test no 211                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 213                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9943.50
 p-value of test no 215                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.84
 p-value of test no 216                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 217                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 218                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.43
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 221                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4900.99
 p-value of test no 222                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 223                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 225                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4844.39
 p-value of test no 226                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4039.39
 p-value of test no 227                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4236.05
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11839.01
 p-value of test no 229                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12019.65
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.06
 p-value of test no 231                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999862562
 
 Normal statistic for number of bits   :   -1.09
 p-value of test no 232                :    0.86
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   38.54
 p-value of test no 233                :    0.94
 
 
 -----------------------------------------------
 Total number of bits:  8000125479
 
 Normal statistic for number of bits   :    0.99
 p-value of test no 234                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 235                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 236                :  1.5e-3
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 237                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.75
 p-value of test no 238                :  3.0e-3
 
 Sample variance                       :    0.57
 p-value of test no 239                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.15
 p-value of test no 243                :    0.56
 
 Sample variance                       :    1.03
 p-value of test no 244                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 245                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 246                :    0.11
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 247                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.90
 p-value of test no 248                :    0.03
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 251                :    0.96
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 252                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.49
 p-value of test no 253                :    0.93
 
 Sample variance                       :    1.16
 p-value of test no 254                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:39.86
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35970
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 4                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 5                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1412
 p-value of test no 6                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334532
   j =  1                              :        599997176
   j =  2                              :             1412
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1406
 p-value of test no 7                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334526
   j =  1                              :        599997188
   j =  2                              :             1406
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 9                  :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 10                 :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 11                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1311
 p-value of test no 12                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334431
   j =  1                              :        599997378
   j =  2                              :             1311
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5441
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4340
 p-value of test no 14                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 16                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4197
 p-value of test no 17                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7236
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7344
 p-value of test no 19                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7305
 p-value of test no 20                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 22                 :    0.9961
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 23                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    1.22
 p-value of test no 24                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    2.07
 p-value of test no 26                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 27                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.61
 p-value of test no 28                 :    0.64
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    1.92
 p-value of test no 30                 :    0.10
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     630
 p-value of test no 31                 :    0.11
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 32                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.94
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.61
 p-value of test no 36                 :    0.64
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     299
 p-value of test no 37                 :    0.51
 
 Stat. AD (mNP2)                       :    2.50
 p-value of test no 38                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    0.68
 p-value of test no 39                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 40                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.91
 p-value of test no 41                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.81
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     151
 p-value of test no 43                 :    0.48
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.10
 p-value of test no 46                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.63
 p-value of test no 47                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.53
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.11
 p-value of test no 49                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.13
 p-value of test no 50                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.03
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.59
 p-value of test no 53                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.71
 p-value of test no 54                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  463.40
 p-value of test no 55                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.43
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6889.37
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 58                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 60                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   32.97
 p-value of test no 61                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 62                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 63                 :    0.26
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 64                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   73.34
 p-value of test no 65                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.03
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   94.92
 p-value of test no 67                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5062.21
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46195
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870195
   j =  1                              :        399907615
   j =  2                              :            46185
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45683
 p-value of test no 71                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869683
   j =  1                              :        399908635
   j =  2                              :            45681
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 72                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 74                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.099
 p-value of test no 76                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 77                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 78                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 79                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.05
 p-value of test no 81                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.044
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 84                 :    0.02
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
 p-value of test no 86                 :    0.9949
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 87                 :    0.02
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 88                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.01e+6
 p-value of test no 89                 :  4.3e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 91                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.060
 p-value of test no 93                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.85
 p-value of test no 95                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 97                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 99                 :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 100                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 101                :    0.70
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 102                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.038
 p-value of test no 104                :    0.92
 
 Anderson-Darling statistic = A2       :    2.51
 p-value of test no 105                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.57
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 108                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
 p-value of test no 109                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    1.60
 p-value of test no 111                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
 p-value of test no 113                :    0.35
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.29
 p-value of test no 115                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.51
 p-value of test no 116                :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.94
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.78
 p-value of test no 119                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.14
 p-value of test no 120                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.71
 p-value of test no 121                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.41
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.68
 p-value of test no 123                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.96
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   37.83
 p-value of test no 125                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 127                :    0.39
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 128                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.90
 p-value of test no 129                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 132                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.29
 p-value of test no 133                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.50
 p-value of test no 134                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.92
 p-value of test no 135                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 136                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.56
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  132.14
 p-value of test no 141                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 142                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.32
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 144                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17579.12
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.97
 p-value of test no 146                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.83
 p-value of test no 147                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.49
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.77
 p-value of test no 150                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.28
 p-value of test no 151                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.10
 p-value of test no 152                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.68
 p-value of test no 153                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.23
 p-value of test no 154                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   30.68
 p-value of test no 155                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.71
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.32
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  495.68
 p-value of test no 158                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  157.13
 p-value of test no 159                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.65
 p-value of test no 160                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.88
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.10
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.18
 p-value of test no 163                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.80
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   93.30
 p-value of test no 165                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  338.23
 p-value of test no 166                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.26
 p-value of test no 167                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4939.42
 p-value of test no 168                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.82
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  152.06
 p-value of test no 170                :    0.9952
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  378.46
 p-value of test no 171                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.52
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5182.50
 p-value of test no 173                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.19
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  225.61
 p-value of test no 175                :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.57
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.88
 p-value of test no 177                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.66
 p-value of test no 178                :    0.88
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.96
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 182                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 183                :    0.45
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 185                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 186                :    0.79
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 187                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.53
 p-value of test no 188                :    0.94
 
 Sample variance                       :    0.35
 p-value of test no 189                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
 p-value of test no 191                :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 192                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
 p-value of test no 194                :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 195                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.51
 p-value of test no 196                :    0.96
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.25
 p-value of test no 198                :    0.41
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
 p-value of test no 200                :    0.9917
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 202                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.38
 p-value of test no 203                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 205                :    0.65
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 206                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.79
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 209                :    0.86
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 210                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9923.21
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 212                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 214                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10171.73
 p-value of test no 215                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 216                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.34
 p-value of test no 217                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.47
 p-value of test no 218                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 219                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.75
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 221                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4845.12
 p-value of test no 222                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 223                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 224                :    0.76
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4847.22
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4162.70
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4094.57
 p-value of test no 228                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11701.96
 p-value of test no 229                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11604.23
 p-value of test no 230                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   82.43
 p-value of test no 231                :  7.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999830087
 
 Normal statistic for number of bits   :   -1.34
 p-value of test no 232                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.03
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999992519
 
 Normal statistic for number of bits   :  -0.059
 p-value of test no 234                :    0.52
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 237                :    0.40
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 238                :    0.19
 
 Sample variance                       :    1.05
 p-value of test no 239                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.76
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 242                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    0.53
 p-value of test no 244                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 245                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 246                :    0.09
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 247                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.04
 p-value of test no 248                :    0.15
 
 Sample variance                       :    0.45
 p-value of test no 249                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 251                :    0.92
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 252                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.04
 p-value of test no 253                :    0.85
 
 Sample variance                       :    1.82
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:10.69
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35971
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 3                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 4                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 5                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1320
 p-value of test no 6                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334440
   j =  1                              :        599997360
   j =  2                              :             1320
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 7                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1374
 p-value of test no 8                  :    0.40
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334494
   j =  1                              :        599997252
   j =  2                              :             1374
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 9                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 10                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1468
 p-value of test no 11                 :  2.8e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334588
   j =  1                              :        599997064
   j =  2                              :             1468
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5198
 p-value of test no 13                 :    0.9988
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 16                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4458
 p-value of test no 17                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7249
 p-value of test no 18                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 19                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7370
 p-value of test no 20                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.36
 p-value of test no 22                 :    0.88
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 23                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 24                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     887
 p-value of test no 25                 :    0.66
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.17
 p-value of test no 28                 :    0.9963
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.36
 p-value of test no 29                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.25
 p-value of test no 30                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.54
 p-value of test no 32                 :    0.71
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 33                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.88
 p-value of test no 34                 :    0.42
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.14
 p-value of test no 35                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 36                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    1.06
 p-value of test no 38                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.74
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.26
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.85
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.80
 p-value of test no 44                 :    0.48
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 45                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:39.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.00
 p-value of test no 46                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   13.67
 p-value of test no 47                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.89
 p-value of test no 48                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.53
 p-value of test no 49                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 50                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.29
 p-value of test no 51                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.36
 p-value of test no 52                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.44
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  261.49
 p-value of test no 54                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  416.93
 p-value of test no 55                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1487.69
 p-value of test no 56                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6993.96
 p-value of test no 57                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.63
 p-value of test no 59                 :  9.0e-3
 
 Anderson-Darling statistic = A2       :    3.84
 p-value of test no 60                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   52.93
 p-value of test no 61                 :  6.0e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 62                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 63                 :    0.23
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 64                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   76.64
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.32
 p-value of test no 66                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  131.87
 p-value of test no 67                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5014.19
 p-value of test no 68                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45738
 p-value of test no 70                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869738
   j =  1                              :        399908531
   j =  2                              :            45724
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46022
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870022
   j =  1                              :        399907961
   j =  2                              :            46012
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 72                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.26
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 76                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 77                 :    0.93
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 78                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 80                 :    0.04
 
 Anderson-Darling statistic = A2       :    2.20
 p-value of test no 81                 :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 83                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 84                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 85                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 88                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 90                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 91                 :    0.87
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 92                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 93                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 97                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 98                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 99                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 100                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.19
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 105                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 106                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 107                :    0.92
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
 p-value of test no 109                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
 p-value of test no 110                :    0.66
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 111                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
 p-value of test no 112                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
 p-value of test no 113                :    0.55
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.93
 p-value of test no 115                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.42
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.23
 p-value of test no 117                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.75
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.26
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.79
 p-value of test no 120                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.80
 p-value of test no 121                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.21
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.59
 p-value of test no 123                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   23.33
 p-value of test no 124                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.56
 p-value of test no 125                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.29
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.78
 p-value of test no 129                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 131                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 132                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.93
 p-value of test no 133                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 134                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.37
 p-value of test no 135                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.12
 p-value of test no 137                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.35
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 140                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.45
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 142                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 144                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17580.03
 p-value of test no 145                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.48
 p-value of test no 146                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.98
 p-value of test no 147                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.14
 p-value of test no 148                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.20
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.64
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.85
 p-value of test no 151                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.22
 p-value of test no 152                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.88
 p-value of test no 153                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.71
 p-value of test no 154                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.14
 p-value of test no 155                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  195.48
 p-value of test no 156                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.37
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  471.62
 p-value of test no 158                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  166.00
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   87.44
 p-value of test no 160                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.16
 p-value of test no 161                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.46
 p-value of test no 162                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.77
 p-value of test no 163                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.77
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   56.33
 p-value of test no 165                :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  443.34
 p-value of test no 166                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  404.89
 p-value of test no 167                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5057.36
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.24
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.39
 p-value of test no 170                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.31
 p-value of test no 171                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  370.00
 p-value of test no 172                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4796.54
 p-value of test no 173                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.43
 p-value of test no 174                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  158.65
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   27.35
 p-value of test no 176                :  6.9e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.34
 p-value of test no 177                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.48
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.18
 p-value of test no 179                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 180                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 181                :  9.2e-3
 
 Anderson-Darling statistic = A2       :    5.30
 p-value of test no 182                :  2.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    3.02
 p-value of test no 183                :  1.3e-3
 
 Sample variance                       :    1.21
 p-value of test no 184                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 185                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 186                :    0.94
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 187                :    0.26
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.56
 p-value of test no 188                :    0.94
 
 Sample variance                       :    2.01
 p-value of test no 189                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
 p-value of test no 193                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.26
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.17
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.34
 p-value of test no 198                :    0.18
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 200                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 201                :    0.88
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 202                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  182.99
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 205                :    0.15
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 206                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.96
 p-value of test no 207                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 208                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.16
 
 Anderson-Darling statistic = A2       :    1.11
 p-value of test no 210                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10165.76
 p-value of test no 211                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 214                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.96
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.22
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.21
 p-value of test no 217                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.60
 p-value of test no 218                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 220                :    0.11
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 221                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4959.06
 p-value of test no 222                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 223                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4767.60
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4161.95
 p-value of test no 227                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4062.69
 p-value of test no 228                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11695.13
 p-value of test no 229                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11488.90
 p-value of test no 230                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   45.06
 p-value of test no 231                :    0.80
 
 
 -----------------------------------------------
 Total number of bits:  8000024220
 
 Normal statistic for number of bits   :    0.19
 p-value of test no 232                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.66
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000026524
 
 Normal statistic for number of bits   :    0.21
 p-value of test no 234                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 235                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 236                :    0.97
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 237                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.48
 p-value of test no 238                :    0.93
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 240                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 241                :    0.85
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.33
 p-value of test no 243                :    0.91
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.32
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 248                :    0.55
 
 Sample variance                       :    0.43
 p-value of test no 249                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.090
 p-value of test no 250                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.51
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 252                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.013
 p-value of test no 253                :    0.49
 
 Sample variance                       :    1.48
 p-value of test no 254                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.78
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:40.25
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35972
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 3                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 4                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 5                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1432
 p-value of test no 6                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334552
   j =  1                              :        599997136
   j =  2                              :             1432
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1322
 p-value of test no 10                 :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334442
   j =  1                              :        599997356
   j =  2                              :             1322
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1447
 p-value of test no 11                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334567
   j =  1                              :        599997106
   j =  2                              :             1447
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1459
 p-value of test no 12                 :  5.7e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334579
   j =  1                              :        599997082
   j =  2                              :             1459
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5442
 p-value of test no 13                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4260
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7268
 p-value of test no 15                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4379
 p-value of test no 16                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4278
 p-value of test no 17                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7244
 p-value of test no 18                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 19                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 20                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7399
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 23                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.43
 p-value of test no 24                 :    0.82
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     913
 p-value of test no 25                 :    0.34
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 26                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 27                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.02
 p-value of test no 28                 :    0.35
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 29                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     609
 p-value of test no 31                 :    0.36
 
 Stat. AD (mNP2)                       :    1.90
 p-value of test no 32                 :    0.10
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.92
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.07
 p-value of test no 35                 :    0.32
 
 Test on the Nm values of W_{n,i}(mNP1):    0.27
 p-value of test no 36                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     302
 p-value of test no 37                 :    0.46
 
 Stat. AD (mNP2)                       :    2.26
 p-value of test no 38                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 39                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.26
 p-value of test no 40                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 41                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 42                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     138
 p-value of test no 43                 :    0.83
 
 Stat. AD (mNP2)                       :    1.65
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.04
 p-value of test no 46                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 47                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.37
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.70
 p-value of test no 49                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.45
 p-value of test no 50                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.91
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.51
 p-value of test no 52                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.87
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  207.03
 p-value of test no 54                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  422.24
 p-value of test no 55                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1421.73
 p-value of test no 56                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7136.12
 p-value of test no 57                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 58                 :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 60                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   23.81
 p-value of test no 61                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 62                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 63                 :    0.87
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 64                 :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   48.38
 p-value of test no 65                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    6.07
 p-value of test no 66                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   97.17
 p-value of test no 67                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5098.16
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45775
 p-value of test no 70                 :    0.69
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869775
   j =  1                              :        399908455
   j =  2                              :            45765
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:30.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46024
 p-value of test no 71                 :    0.25
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870024
   j =  1                              :        399907960
   j =  2                              :            46008
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 72                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 73                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.79
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 76                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 77                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 78                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 79                 :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 81                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.38
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 85                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 86                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 88                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.08
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 90                 :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 92                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 94                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.025
 p-value of test no 98                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 99                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 100                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.028
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 102                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 103                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 105                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.53
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 108                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.90e-5
 p-value of test no 109                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 111                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
 p-value of test no 112                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
 p-value of test no 113                :    0.79
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 114                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 115                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      : -4.58e-3
 p-value of test no 116                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 117                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.04
 p-value of test no 118                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.23
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.70
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.29
 p-value of test no 121                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   57.76
 p-value of test no 122                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.70
 p-value of test no 123                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.72
 p-value of test no 124                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   10.72
 p-value of test no 125                :    0.9992    *****
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.45
 p-value of test no 126                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 128                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.44
 p-value of test no 129                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 132                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.51
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.31
 p-value of test no 134                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 135                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.06
 p-value of test no 137                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 138                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.027
 p-value of test no 139                :    0.97
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 140                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.91
 p-value of test no 141                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 142                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.53
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 144                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17505.62
 p-value of test no 145                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   56.01
 p-value of test no 146                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   34.34
 p-value of test no 147                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.00
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.30
 p-value of test no 149                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.15
 p-value of test no 150                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.77
 p-value of test no 151                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.20
 p-value of test no 152                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.65
 p-value of test no 153                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.10
 p-value of test no 154                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.29
 p-value of test no 155                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.82
 p-value of test no 156                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.43
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.64
 p-value of test no 158                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.29
 p-value of test no 159                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.63
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.88
 p-value of test no 161                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.06
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  530.27
 p-value of test no 163                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  125.88
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.24
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.18
 p-value of test no 166                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.56
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.78
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  421.81
 p-value of test no 169                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.90
 p-value of test no 170                :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.00
 p-value of test no 171                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.00
 p-value of test no 172                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5043.27
 p-value of test no 173                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.27
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  177.90
 p-value of test no 175                :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   18.64
 p-value of test no 176                :    0.10
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :  -0.010
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.06
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.14
 p-value of test no 179                :    0.87
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 180                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 181                :    0.29
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 182                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.62
 p-value of test no 183                :    0.27
 
 Sample variance                       :    0.56
 p-value of test no 184                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 187                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.54
 p-value of test no 188                :    0.70
 
 Sample variance                       :    0.56
 p-value of test no 189                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
 p-value of test no 190                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 192                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
 p-value of test no 193                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
 p-value of test no 194                :    0.47
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 195                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.84
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.18
 p-value of test no 198                :    0.92
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 200                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 201                :    0.94
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.14
 p-value of test no 203                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 204                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  222.86
 p-value of test no 207                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 208                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 210                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10274.66
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 213                :    0.18
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 214                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10161.48
 p-value of test no 215                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.03
 p-value of test no 216                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.27
 p-value of test no 217                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 218                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 220                :    0.76
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 221                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4916.95
 p-value of test no 222                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 223                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 224                :    0.69
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 225                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4770.55
 p-value of test no 226                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4254.66
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4076.43
 p-value of test no 228                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11885.62
 p-value of test no 229                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12003.68
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.48
 p-value of test no 231                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000058735
 
 Normal statistic for number of bits   :    0.46
 p-value of test no 232                :    0.32
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.72
 p-value of test no 233                :    0.28
 
 
 -----------------------------------------------
 Total number of bits:  7999873968
 
 Normal statistic for number of bits   :   -1.00
 p-value of test no 234                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 235                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 236                :    0.99
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 237                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.27
 p-value of test no 238                :    0.90
 
 Sample variance                       :    1.03
 p-value of test no 239                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 240                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.19
 p-value of test no 243                :    0.88
 
 Sample variance                       :    1.88
 p-value of test no 244                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 245                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 246                :    0.04
 
 Anderson-Darling statistic = A2       :    2.84
 p-value of test no 247                :    0.03
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.29
 p-value of test no 248                :    0.01
 
 Sample variance                       :    0.84
 p-value of test no 249                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.44
 p-value of test no 253                :    0.67
 
 Sample variance                       :    0.58
 p-value of test no 254                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.07
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:54.38
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  65  SumCollector                    0.9992 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35973
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.16
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1410
 p-value of test no 5                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334530
   j =  1                              :        599997180
   j =  2                              :             1410
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 6                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1427
 p-value of test no 7                  :    0.05
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334547
   j =  1                              :        599997146
   j =  2                              :             1427
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 8                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 9                  :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 10                 :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 11                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 12                 :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5354
 p-value of test no 13                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4319
 p-value of test no 14                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4277
 p-value of test no 16                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4353
 p-value of test no 17                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 18                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7169
 p-value of test no 19                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7382
 p-value of test no 20                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7430
 p-value of test no 21                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.73
 p-value of test no 23                 :    0.53
 
 Test on the Nm values of W_{n,i}(mNP1):    2.00
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 26                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 28                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.94
 p-value of test no 29                 :    0.39
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 30                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     622
 p-value of test no 31                 :    0.19
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 32                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.85
 p-value of test no 33                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 34                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     292
 p-value of test no 37                 :    0.66
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 38                 :    0.17
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 41                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     148
 p-value of test no 43                 :    0.54
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 44                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    4.09
 p-value of test no 45                 :  7.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.48
 p-value of test no 46                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.16
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.63
 p-value of test no 48                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.44
 p-value of test no 49                 :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.95
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.79
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.27
 p-value of test no 52                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.16
 p-value of test no 53                 :  6.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  251.48
 p-value of test no 54                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.40
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1448.68
 p-value of test no 56                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7016.46
 p-value of test no 57                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 60                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.76
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 62                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 63                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 64                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   59.88
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.19
 p-value of test no 66                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  112.56
 p-value of test no 67                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4881.79
 p-value of test no 68                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46083
 p-value of test no 70                 :    0.17
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870083
   j =  1                              :        399907837
   j =  2                              :            46077
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45421
 p-value of test no 71                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869421
   j =  1                              :        399909159
   j =  2                              :            45419
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 73                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 74                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.46
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.027
 p-value of test no 76                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 77                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 78                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 79                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 80                 :    0.21
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 81                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 83                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 84                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.46
 p-value of test no 85                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 88                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 90                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 91                 :    0.78
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 94                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.60
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.031
 p-value of test no 97                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 98                 :    0.17
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 99                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 101                :    0.74
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 104                :    0.18
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 105                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 108                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
 p-value of test no 110                :    0.88
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 111                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
 p-value of test no 112                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
 p-value of test no 113                :    0.86
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.62
 p-value of test no 115                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 116                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 117                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 118                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.08
 p-value of test no 119                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   78.83
 p-value of test no 120                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   89.86
 p-value of test no 121                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.83
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.31
 p-value of test no 123                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   44.85
 p-value of test no 124                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.37
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 126                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 127                :    0.31
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 128                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.96
 p-value of test no 129                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.66
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 132                :    0.9927
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.14
 p-value of test no 133                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.37
 p-value of test no 134                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.27
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.075
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.56
 p-value of test no 137                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 138                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 139                :    0.22
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 140                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  141.80
 p-value of test no 141                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 144                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17544.19
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   42.53
 p-value of test no 146                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.14
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.77
 p-value of test no 148                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.14
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.82
 p-value of test no 150                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.17
 p-value of test no 151                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   46.77
 p-value of test no 152                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.82
 p-value of test no 153                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.93
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    5.50
 p-value of test no 155                :    0.9960
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.26
 p-value of test no 156                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.03
 p-value of test no 157                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.85
 p-value of test no 158                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  123.08
 p-value of test no 159                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.76
 p-value of test no 160                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  167.06
 p-value of test no 161                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.06
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.39
 p-value of test no 163                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.84
 p-value of test no 164                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   98.06
 p-value of test no 165                :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.45
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.11
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4998.73
 p-value of test no 168                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  331.23
 p-value of test no 169                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  211.65
 p-value of test no 170                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.46
 p-value of test no 171                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.64
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4979.88
 p-value of test no 173                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  329.76
 p-value of test no 174                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.70
 p-value of test no 175                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.33
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.31
 p-value of test no 177                :    0.62
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.30
 p-value of test no 178                :    0.59
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 180                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 181                :    0.17
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.16
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.00
 p-value of test no 184                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 185                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.66
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 187                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.57
 p-value of test no 188                :    0.71
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
 p-value of test no 191                :    0.95
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
 p-value of test no 194                :    0.62
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 195                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.80
 p-value of test no 196                :    0.36
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.31
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 200                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 201                :    0.20
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  214.97
 p-value of test no 203                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 204                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 205                :    0.49
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.49
 p-value of test no 207                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 208                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 209                :    0.83
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9904.41
 p-value of test no 211                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 212                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 214                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10111.56
 p-value of test no 215                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.23
 p-value of test no 216                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.15
 p-value of test no 218                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 219                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 220                :    0.05
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 221                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5038.10
 p-value of test no 222                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 224                :    0.77
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 225                :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4836.96
 p-value of test no 226                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4119.48
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4214.69
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11892.35
 p-value of test no 229                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11824.06
 p-value of test no 230                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.96
 p-value of test no 231                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  7999930131
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.01
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  7999938360
 
 Normal statistic for number of bits   :   -0.49
 p-value of test no 234                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.076
 p-value of test no 236                :    0.85
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.84
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 238                :    0.72
 
 Sample variance                       :    1.51
 p-value of test no 239                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 240                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 242                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.67
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.76
 p-value of test no 244                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 245                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 246                :    0.96
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 247                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.12
 p-value of test no 248                :    0.87
 
 Sample variance                       :    0.90
 p-value of test no 249                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 250                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.58
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 252                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.22
 p-value of test no 253                :    0.41
 
 Sample variance                       :    1.21
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.06
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.93
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35974
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 3                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1286
 p-value of test no 4                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334406
   j =  1                              :        599997428
   j =  2                              :             1286
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:11.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 5                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 6                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 7                  :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1449
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334569
   j =  1                              :        599997102
   j =  2                              :             1449
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 11                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5461
 p-value of test no 13                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4402
 p-value of test no 14                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7444
 p-value of test no 15                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 16                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4329
 p-value of test no 17                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 19                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7358
 p-value of test no 20                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7222
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 22                 :    0.49
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.41
 p-value of test no 23                 :    0.20
 
 Test on the Nm values of W_{n,i}(mNP1):    0.72
 p-value of test no 24                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     900
 p-value of test no 25                 :    0.50
 
 Stat. AD (mNP2)                       :    0.57
 p-value of test no 26                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    1.35
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.19
 p-value of test no 28                 :    0.07
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.55
 p-value of test no 29                 :    0.16
 
 Test on the Nm values of W_{n,i}(mNP1):    1.81
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     576
 p-value of test no 31                 :    0.83
 
 Stat. AD (mNP2)                       :    2.13
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    3.25
 p-value of test no 33                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 34                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.51
 p-value of test no 35                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    0.74
 p-value of test no 36                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 39                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 40                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 41                 :    0.89
 
 Test on the Nm values of W_{n,i}(mNP1):    1.52
 p-value of test no 42                 :    0.17
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     124
 p-value of test no 43                 :    0.98
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 44                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.48
 p-value of test no 45                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.79
 p-value of test no 46                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.80
 p-value of test no 47                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.71
 p-value of test no 48                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.66
 p-value of test no 49                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.57
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.66
 p-value of test no 51                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.31
 p-value of test no 52                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.37
 p-value of test no 53                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  213.89
 p-value of test no 54                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  442.57
 p-value of test no 55                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1316.03
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7011.36
 p-value of test no 57                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 58                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 59                 :    0.54
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.07
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 62                 :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 64                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.98
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  110.76
 p-value of test no 67                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5151.26
 p-value of test no 68                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45505
 p-value of test no 70                 :    0.96
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869505
   j =  1                              :        399908994
   j =  2                              :            45497
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46168
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870168
   j =  1                              :        399907665
   j =  2                              :            46166
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.56
 p-value of test no 74                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.12
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 76                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 78                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 79                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 81                 :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 85                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 86                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 88                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 90                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 94                 :    0.10
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 95                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.54
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 97                 :  3.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    3.99
 p-value of test no 99                 :  9.0e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.36
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 103                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 105                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.43
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 108                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
 p-value of test no 109                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
 p-value of test no 110                :    0.19
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 111                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
 p-value of test no 112                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 114                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.88
 p-value of test no 115                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.18
 p-value of test no 116                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 118                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.43
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.34
 p-value of test no 120                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   44.81
 p-value of test no 121                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.97
 p-value of test no 122                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   34.82
 p-value of test no 123                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.96
 p-value of test no 124                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   38.74
 p-value of test no 125                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 128                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.83
 p-value of test no 129                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.63
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 132                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.43
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.22
 p-value of test no 134                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.09
 p-value of test no 135                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.18
 p-value of test no 136                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.30
 p-value of test no 137                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 139                :    0.33
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  135.69
 p-value of test no 141                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 143                :    0.71
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17282.70
 p-value of test no 145                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.02
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.96
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.08
 p-value of test no 148                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   34.60
 p-value of test no 149                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.92
 p-value of test no 150                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   26.15
 p-value of test no 151                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.88
 p-value of test no 152                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   15.27
 p-value of test no 153                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.99
 p-value of test no 154                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    6.93
 p-value of test no 155                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.86
 p-value of test no 156                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.36
 p-value of test no 157                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.80
 p-value of test no 158                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.62
 p-value of test no 159                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.16
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.70
 p-value of test no 161                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.79
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.83
 p-value of test no 163                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.17
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   77.71
 p-value of test no 165                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.24
 p-value of test no 166                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  375.75
 p-value of test no 167                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4805.73
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.61
 p-value of test no 169                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  179.94
 p-value of test no 170                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  429.30
 p-value of test no 171                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.73
 p-value of test no 172                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5270.45
 p-value of test no 173                :  3.9e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  378.66
 p-value of test no 174                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.65
 p-value of test no 175                :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.63
 p-value of test no 176                :    0.48
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.29
 p-value of test no 177                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.36
 p-value of test no 178                :    0.67
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.43
 p-value of test no 179                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 180                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.090
 p-value of test no 181                :    0.80
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 182                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.61
 p-value of test no 183                :    0.95
 
 Sample variance                       :    0.58
 p-value of test no 184                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 185                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 186                :    0.84
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.26
 p-value of test no 188                :    0.90
 
 Sample variance                       :    0.44
 p-value of test no 189                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 190                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.35
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 192                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 193                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
 p-value of test no 194                :    0.70
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 195                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.71
 p-value of test no 196                :    0.06
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.34
 p-value of test no 198                :    0.40
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 200                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 201                :    0.83
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  181.18
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 205                :    0.18
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 206                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.99
 p-value of test no 207                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 208                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 209                :    0.89
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 210                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9840.98
 p-value of test no 211                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.60
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 214                :    0.99
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10043.37
 p-value of test no 215                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.46
 p-value of test no 216                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 217                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.65
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 219                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 220                :    0.01
 
 Anderson-Darling statistic = A2       :    3.62
 p-value of test no 221                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5153.08
 p-value of test no 222                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 223                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.59
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 225                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4784.75
 p-value of test no 226                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4037.77
 p-value of test no 227                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4219.90
 p-value of test no 228                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11641.08
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11846.29
 p-value of test no 230                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   52.12
 p-value of test no 231                :    0.55
 
 
 -----------------------------------------------
 Total number of bits:  8000097042
 
 Normal statistic for number of bits   :    0.77
 p-value of test no 232                :    0.22
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   55.90
 p-value of test no 233                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  8000068110
 
 Normal statistic for number of bits   :    0.54
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 238                :    0.37
 
 Sample variance                       :    1.47
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 240                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 241                :    0.12
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 242                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 243                :    0.22
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 245                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 246                :    0.22
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 247                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.42
 p-value of test no 248                :    0.08
 
 Sample variance                       :    1.65
 p-value of test no 249                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 250                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.46
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 252                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.60
 p-value of test no 253                :    0.27
 
 Sample variance                       :    1.20
 p-value of test no 254                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.70
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:45.87
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35975
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :  2.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 3                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 5                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1407
 p-value of test no 6                  :    0.13
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334527
   j =  1                              :        599997186
   j =  2                              :             1407
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1391
 p-value of test no 7                  :    0.24
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334511
   j =  1                              :        599997218
   j =  2                              :             1391
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 8                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 9                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 10                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 11                 :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1300
 p-value of test no 12                 :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334420
   j =  1                              :        599997400
   j =  2                              :             1300
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5287
 p-value of test no 13                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4318
 p-value of test no 14                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 15                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4396
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7323
 p-value of test no 18                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 20                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 21                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 22                 :    0.31
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.76
 p-value of test no 24                 :    0.51
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    2.16
 p-value of test no 26                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.19
 p-value of test no 27                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 28                 :    0.33
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.87
 p-value of test no 29                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     611
 p-value of test no 31                 :    0.33
 
 Stat. AD (mNP2)                       :    1.36
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.49
 p-value of test no 33                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.70
 p-value of test no 34                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.63
 p-value of test no 36                 :    0.62
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    1.70
 p-value of test no 38                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.76
 p-value of test no 39                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.43
 p-value of test no 40                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.31
 p-value of test no 41                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 42                 :    0.87
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    1.11
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 45                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.39
 p-value of test no 46                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.38
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.08
 p-value of test no 48                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   11.82
 p-value of test no 49                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.32
 p-value of test no 50                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.41
 p-value of test no 51                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.80
 p-value of test no 52                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.43
 p-value of test no 53                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  244.40
 p-value of test no 54                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  415.45
 p-value of test no 55                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1465.41
 p-value of test no 56                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7047.87
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 58                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 60                 :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.31
 p-value of test no 61                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.92
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.48
 p-value of test no 66                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.46
 p-value of test no 67                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5132.13
 p-value of test no 68                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46092
 p-value of test no 70                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870092
   j =  1                              :        399907820
   j =  2                              :            46084
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45707
 p-value of test no 71                 :    0.79
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869707
   j =  1                              :        399908592
   j =  2                              :            45695
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 72                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 74                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 78                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 80                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 83                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 84                 :    0.09
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 86                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 88                 :    0.36
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.22
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.35
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 95                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 97                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 98                 :    0.87
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 100                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 102                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 103                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 105                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 107                :    0.82
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
 p-value of test no 109                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
 p-value of test no 110                :    0.46
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 111                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
 p-value of test no 112                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
 p-value of test no 113                :    0.29
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 114                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.25
 p-value of test no 115                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 116                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.036
 p-value of test no 117                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.029
 p-value of test no 118                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   90.34
 p-value of test no 119                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.77
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.02
 p-value of test no 121                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.16
 p-value of test no 122                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.85
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   55.51
 p-value of test no 124                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.73
 p-value of test no 125                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 127                :    0.19
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 128                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.40
 p-value of test no 129                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 130                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.54
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 132                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.66
 p-value of test no 133                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.32
 p-value of test no 134                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.31
 p-value of test no 135                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.08
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.34
 p-value of test no 137                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 139                :    0.46
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 140                :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.17
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 142                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.23
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 144                :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17541.42
 p-value of test no 145                :    0.27
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.64
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.73
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   37.33
 p-value of test no 148                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.54
 p-value of test no 149                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.25
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.56
 p-value of test no 151                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   53.75
 p-value of test no 152                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.48
 p-value of test no 153                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   11.24
 p-value of test no 154                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.05
 p-value of test no 155                :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  136.60
 p-value of test no 156                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.55
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  528.81
 p-value of test no 158                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.67
 p-value of test no 159                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   69.98
 p-value of test no 160                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.59
 p-value of test no 161                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.66
 p-value of test no 162                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  486.58
 p-value of test no 163                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  116.97
 p-value of test no 164                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   83.50
 p-value of test no 165                :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.47
 p-value of test no 166                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.21
 p-value of test no 167                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4949.45
 p-value of test no 168                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  388.67
 p-value of test no 169                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.99
 p-value of test no 170                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  361.29
 p-value of test no 171                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.03
 p-value of test no 172                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5016.29
 p-value of test no 173                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  381.48
 p-value of test no 174                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  207.54
 p-value of test no 175                :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.79
 p-value of test no 176                :    0.80
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.60
 p-value of test no 177                :    0.94
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.44
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.45
 p-value of test no 179                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 181                :    0.96
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.17
 p-value of test no 183                :    0.88
 
 Sample variance                       :    0.97
 p-value of test no 184                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 185                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 186                :    0.11
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 187                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.61
 p-value of test no 188                :    0.05
 
 Sample variance                       :    0.88
 p-value of test no 189                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 190                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
 p-value of test no 191                :    0.62
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 192                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 194                :    0.08
 
 Anderson-Darling statistic = A2       :    1.44
 p-value of test no 195                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.14
 p-value of test no 196                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 197                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.84
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 200                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    2.27
 p-value of test no 202                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  240.77
 p-value of test no 203                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 204                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 205                :    0.98
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 206                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  167.31
 p-value of test no 207                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 208                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.59
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 210                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10081.15
 p-value of test no 211                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 212                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.52
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10071.19
 p-value of test no 215                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.36
 p-value of test no 216                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.19
 p-value of test no 217                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.25
 p-value of test no 218                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 219                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 220                :    0.38
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 221                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4881.74
 p-value of test no 222                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 223                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 224                :    0.14
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 225                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4905.52
 p-value of test no 226                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3948.72
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4130.78
 p-value of test no 228                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11960.92
 p-value of test no 229                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11863.24
 p-value of test no 230                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.63
 p-value of test no 231                :    0.03
 
 
 -----------------------------------------------
 Total number of bits:  7999841664
 
 Normal statistic for number of bits   :   -1.25
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   74.00
 p-value of test no 233                :    0.04
 
 
 -----------------------------------------------
 Total number of bits:  7999999833
 
 Normal statistic for number of bits   : -1.32e-3
 p-value of test no 234                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.81
 p-value of test no 238                :    0.21
 
 Sample variance                       :    1.02
 p-value of test no 239                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.66
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 243                :    0.57
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 245                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 246                :    0.77
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 247                :    0.98
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.32
 p-value of test no 248                :    0.63
 
 Sample variance                       :    1.27
 p-value of test no 249                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 250                :    0.9921
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 251                :    0.09
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.81
 p-value of test no 253                :    0.04
 
 Sample variance                       :    0.91
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.04
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.68
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35976
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 3                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 4                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 5                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1421
 p-value of test no 6                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334541
   j =  1                              :        599997158
   j =  2                              :             1421
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 7                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 8                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1329
 p-value of test no 9                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334449
   j =  1                              :        599997342
   j =  2                              :             1329
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1446
 p-value of test no 10                 :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334566
   j =  1                              :        599997108
   j =  2                              :             1446
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 11                 :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 12                 :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5390
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 14                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 15                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4248
 p-value of test no 16                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4341
 p-value of test no 17                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7389
 p-value of test no 18                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 19                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7200
 p-value of test no 20                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:05.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7187
 p-value of test no 21                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.28
 p-value of test no 23                 :    0.95
 
 Test on the Nm values of W_{n,i}(mNP1):    0.19
 p-value of test no 24                 :    0.9931
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     907
 p-value of test no 25                 :    0.41
 
 Stat. AD (mNP2)                       :    0.96
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.11
 p-value of test no 27                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.54
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.65
 p-value of test no 30                 :    0.60
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.40
 p-value of test no 32                 :    0.85
 
 Stat. AD after spacings (mNP2-S)      :    4.48
 p-value of test no 33                 :  5.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.68
 p-value of test no 35                 :    0.58
 
 Test on the Nm values of W_{n,i}(mNP1):    0.39
 p-value of test no 36                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 38                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    0.45
 p-value of test no 39                 :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 40                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.17
 p-value of test no 41                 :    0.28
 
 Test on the Nm values of W_{n,i}(mNP1):    0.30
 p-value of test no 42                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     161
 p-value of test no 43                 :    0.19
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 44                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.98
 p-value of test no 46                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.37
 p-value of test no 47                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.95
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.93
 p-value of test no 49                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.87
 p-value of test no 50                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.28
 p-value of test no 51                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   62.46
 p-value of test no 52                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.47
 p-value of test no 53                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  252.23
 p-value of test no 54                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.20
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1492.56
 p-value of test no 56                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7204.29
 p-value of test no 57                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 58                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.54
 p-value of test no 59                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.70
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.54
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 62                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 64                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   72.20
 p-value of test no 65                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.21
 p-value of test no 66                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  125.17
 p-value of test no 67                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5220.44
 p-value of test no 68                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46054
 p-value of test no 70                 :    0.21
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870054
   j =  1                              :        399907893
   j =  2                              :            46052
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45957
 p-value of test no 71                 :    0.36
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869957
   j =  1                              :        399908092
   j =  2                              :            45945
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 73                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 77                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 78                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 81                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.76
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 83                 :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 84                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 85                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 86                 :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 88                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.21
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 90                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 91                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 92                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 93                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 94                 :    0.96
 
 Anderson-Darling statistic = A2       :    2.47
 p-value of test no 95                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.98
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 99                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 101                :    0.83
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 102                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 104                :    0.74
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 105                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 106                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 108                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
 p-value of test no 109                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    : 3.10e-5
 p-value of test no 110                :    0.96
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 111                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
 p-value of test no 112                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 5.33e-5
 p-value of test no 113                :    0.89
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 114                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.16
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.95
 p-value of test no 117                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.14
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.83
 p-value of test no 119                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   70.95
 p-value of test no 120                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.75
 p-value of test no 121                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   21.06
 p-value of test no 122                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.47
 p-value of test no 123                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.44
 p-value of test no 124                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   31.48
 p-value of test no 125                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 126                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.45
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.36
 p-value of test no 129                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 130                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 131                :    0.68
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 132                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.07
 p-value of test no 133                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.00
 p-value of test no 134                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.16
 p-value of test no 135                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.21
 p-value of test no 136                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.34
 p-value of test no 137                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 138                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.68
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 140                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  114.30
 p-value of test no 141                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 143                :    0.19
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17526.33
 p-value of test no 145                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.25
 p-value of test no 146                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   38.24
 p-value of test no 147                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   14.89
 p-value of test no 148                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.57
 p-value of test no 149                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.55
 p-value of test no 150                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.87
 p-value of test no 151                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.80
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.02
 p-value of test no 153                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.14
 p-value of test no 154                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.76
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.67
 p-value of test no 156                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  165.41
 p-value of test no 157                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.71
 p-value of test no 158                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.25
 p-value of test no 159                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.31
 p-value of test no 160                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.31
 p-value of test no 161                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.36
 p-value of test no 162                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  516.89
 p-value of test no 163                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.63
 p-value of test no 164                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   51.91
 p-value of test no 165                :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.73
 p-value of test no 166                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.56
 p-value of test no 167                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4787.51
 p-value of test no 168                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  462.83
 p-value of test no 169                :  1.8e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.55
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.89
 p-value of test no 171                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.85
 p-value of test no 172                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5002.40
 p-value of test no 173                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.49
 p-value of test no 174                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.53
 p-value of test no 175                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.42
 p-value of test no 176                :    0.83
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.79
 p-value of test no 177                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.13
 p-value of test no 178                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.17
 p-value of test no 179                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 180                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 183                :    0.68
 
 Sample variance                       :    0.98
 p-value of test no 184                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 185                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 186                :    0.38
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 187                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 188                :    0.66
 
 Sample variance                       :    0.53
 p-value of test no 189                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 190                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 192                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 194                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 195                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   17.17
 p-value of test no 196                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.52
 p-value of test no 198                :    0.48
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 200                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 201                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.03
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.55
 p-value of test no 204                :  1.3e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 1.13e-3
 p-value of test no 205                :    0.9989
 
 Anderson-Darling statistic = A2       :    5.02
 p-value of test no 206                :  3.0e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  141.74
 p-value of test no 207                :    0.9994    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 208                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.64
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9944.55
 p-value of test no 211                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 213                :    0.49
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 214                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10064.01
 p-value of test no 215                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.73
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.68
 p-value of test no 217                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 218                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 220                :    0.18
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 221                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4967.89
 p-value of test no 222                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.57
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4846.90
 p-value of test no 226                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.29
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4112.00
 p-value of test no 228                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11725.62
 p-value of test no 229                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11850.35
 p-value of test no 230                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   66.06
 p-value of test no 231                :    0.13
 
 
 -----------------------------------------------
 Total number of bits:  8000128176
 
 Normal statistic for number of bits   :    1.01
 p-value of test no 232                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   37.72
 p-value of test no 233                :    0.95
 
 
 -----------------------------------------------
 Total number of bits:  7999947522
 
 Normal statistic for number of bits   :   -0.41
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.060
 p-value of test no 236                :    0.90
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 237                :    0.76
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 238                :    0.77
 
 Sample variance                       :    0.75
 p-value of test no 239                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.067
 p-value of test no 241                :    0.88
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 242                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.66
 p-value of test no 243                :    0.75
 
 Sample variance                       :    0.80
 p-value of test no 244                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 245                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 246                :    0.16
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 247                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.28
 p-value of test no 248                :    0.10
 
 Sample variance                       :    0.53
 p-value of test no 249                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.046
 p-value of test no 251                :    0.93
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 252                :    0.72
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 253                :    0.77
 
 Sample variance                       :    0.89
 p-value of test no 254                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.84
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:40.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  89  PeriodsInStrings, r = 20        0.9994 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35977
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1339
 p-value of test no 3                  :    0.75
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334459
   j =  1                              :        599997322
   j =  2                              :             1339
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 4                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 6                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 7                  :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1304
 p-value of test no 8                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334424
   j =  1                              :        599997392
   j =  2                              :             1304
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 10                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1400
 p-value of test no 11                 :    0.17
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334520
   j =  1                              :        599997200
   j =  2                              :             1400
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 12                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:54.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5381
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4448
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7339
 p-value of test no 15                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4383
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 17                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7237
 p-value of test no 18                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7301
 p-value of test no 19                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7412
 p-value of test no 20                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7396
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.45
 p-value of test no 22                 :    0.19
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.52
 p-value of test no 23                 :    0.17
 
 Test on the Nm values of W_{n,i}(mNP1):    1.13
 p-value of test no 24                 :    0.30
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     918
 p-value of test no 25                 :    0.28
 
 Stat. AD (mNP2)                       :    1.07
 p-value of test no 26                 :    0.32
 
 Stat. AD after spacings (mNP2-S)      :    0.89
 p-value of test no 27                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.27
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.62
 p-value of test no 29                 :    0.15
 
 Test on the Nm values of W_{n,i}(mNP1):    1.32
 p-value of test no 30                 :    0.22
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     642
 p-value of test no 31                 :    0.05
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 33                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.71
 p-value of test no 34                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 36                 :    0.94
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     312
 p-value of test no 37                 :    0.25
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 39                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.47
 p-value of test no 40                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 41                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 42                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    2.60
 p-value of test no 44                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.52
 p-value of test no 45                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.31
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.31
 p-value of test no 47                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.47
 p-value of test no 48                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.09
 p-value of test no 49                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.67
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.82
 p-value of test no 51                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   64.19
 p-value of test no 52                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.44
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  211.48
 p-value of test no 54                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.20
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1520.20
 p-value of test no 56                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7211.89
 p-value of test no 57                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 58                 :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 59                 :    0.57
 
 Anderson-Darling statistic = A2       :    2.04
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.29
 p-value of test no 61                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 62                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 64                 :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.72
 p-value of test no 65                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.16
 p-value of test no 66                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.79
 p-value of test no 67                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4896.95
 p-value of test no 68                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45596
 p-value of test no 70                 :    0.91
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869596
   j =  1                              :        399908809
   j =  2                              :            45594
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45945
 p-value of test no 71                 :    0.38
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869945
   j =  1                              :        399908118
   j =  2                              :            45929
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 72                 :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 73                 :    0.32
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 74                 :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 76                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 78                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.025
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 80                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 81                 :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.46
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 85                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 86                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :   0.099
 p-value of test no 87                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 88                 :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 90                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 92                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 94                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 97                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 98                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 99                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 101                :    0.64
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 102                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 105                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 107                :    0.67
 
 Anderson-Darling statistic = A2       :    0.48
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
 p-value of test no 109                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    : 1.89e-5
 p-value of test no 110                :    0.99
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 111                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 112                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 114                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.66
 p-value of test no 115                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.75
 p-value of test no 116                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      : 7.42e-3
 p-value of test no 117                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.32
 p-value of test no 118                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.94
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.54
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.19
 p-value of test no 121                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   24.66
 p-value of test no 122                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   52.06
 p-value of test no 123                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   17.43
 p-value of test no 124                :    0.9974
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   16.69
 p-value of test no 125                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 127                :    0.34
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 128                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   49.51
 p-value of test no 129                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 131                :    0.84
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 132                :    0.9975
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.88
 p-value of test no 133                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.19
 p-value of test no 134                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.62
 p-value of test no 135                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 137                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 138                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.33
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 142                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.26
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 144                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17651.07
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 146                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.33
 p-value of test no 147                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.40
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.84
 p-value of test no 149                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.69
 p-value of test no 150                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   39.79
 p-value of test no 151                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   42.57
 p-value of test no 152                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.74
 p-value of test no 153                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.78
 p-value of test no 154                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 155                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  122.81
 p-value of test no 156                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.34
 p-value of test no 157                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.05
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  144.77
 p-value of test no 159                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.10
 p-value of test no 160                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.82
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.77
 p-value of test no 162                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  555.18
 p-value of test no 163                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  142.18
 p-value of test no 164                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   57.65
 p-value of test no 165                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  342.65
 p-value of test no 166                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  396.39
 p-value of test no 167                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5024.83
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  391.56
 p-value of test no 169                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.21
 p-value of test no 170                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  424.70
 p-value of test no 171                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.27
 p-value of test no 172                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4876.01
 p-value of test no 173                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.11
 p-value of test no 174                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  230.88
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.03
 p-value of test no 176                :    0.19
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.53
 p-value of test no 177                :    0.06
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.00
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.83
 p-value of test no 179                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 180                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 181                :    0.82
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.91
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.52
 p-value of test no 184                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 186                :    0.02
 
 Anderson-Darling statistic = A2       :    2.08
 p-value of test no 187                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.47
 p-value of test no 188                :    0.07
 
 Sample variance                       :    0.27
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
 p-value of test no 191                :    0.55
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 192                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 194                :    0.12
 
 Anderson-Darling statistic = A2       :    1.62
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.30
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.80
 p-value of test no 198                :    0.45
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 199                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 200                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 201                :    0.41
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 202                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  216.42
 p-value of test no 203                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 205                :    0.82
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 206                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  189.21
 p-value of test no 207                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 208                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 209                :    0.79
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 210                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9967.90
 p-value of test no 211                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 212                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.16
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 214                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9994.88
 p-value of test no 215                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.99
 p-value of test no 216                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 217                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.44
 p-value of test no 218                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 219                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.52
 p-value of test no 220                :  2.3e-3
 
 Anderson-Darling statistic = A2       :    2.94
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5078.06
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 223                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4889.24
 p-value of test no 226                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.21
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.01
 p-value of test no 228                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.99
 p-value of test no 229                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11708.13
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.83
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  8000006376
 
 Normal statistic for number of bits   :   0.050
 p-value of test no 232                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.17
 p-value of test no 233                :    0.73
 
 
 -----------------------------------------------
 Total number of bits:  7999965690
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 235                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.39
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 237                :    0.39
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.50
 p-value of test no 238                :    0.69
 
 Sample variance                       :    0.32
 p-value of test no 239                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 240                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 242                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.30
 p-value of test no 243                :    0.38
 
 Sample variance                       :    2.15
 p-value of test no 244                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 245                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 246                :    0.78
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 247                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    0.87
 p-value of test no 249                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 250                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 251                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.59
 p-value of test no 253                :    0.72
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.71
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:48.26
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35978
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1355
 p-value of test no 3                  :    0.59
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334475
   j =  1                              :        599997290
   j =  2                              :             1355
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 4                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:34.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1376
 p-value of test no 7                  :    0.38
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334496
   j =  1                              :        599997248
   j =  2                              :             1376
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:42.91
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 8                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1363
 p-value of test no 9                  :    0.51
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334483
   j =  1                              :        599997274
   j =  2                              :             1363
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 10                 :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 12                 :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4391
 p-value of test no 14                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7322
 p-value of test no 15                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4315
 p-value of test no 16                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4380
 p-value of test no 17                 :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 18                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7398
 p-value of test no 19                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:36.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7357
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7402
 p-value of test no 21                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.98
 p-value of test no 22                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 23                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    0.69
 p-value of test no 24                 :    0.57
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     902
 p-value of test no 25                 :    0.48
 
 Stat. AD (mNP2)                       :    1.10
 p-value of test no 26                 :    0.31
 
 Stat. AD after spacings (mNP2-S)      :    0.41
 p-value of test no 27                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.06
 p-value of test no 28                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.81
 p-value of test no 29                 :    0.12
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 30                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     627
 p-value of test no 31                 :    0.14
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 32                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.07
 p-value of test no 34                 :    0.32
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.51
 p-value of test no 35                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     298
 p-value of test no 37                 :    0.53
 
 Stat. AD (mNP2)                       :    2.08
 p-value of test no 38                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.73
 p-value of test no 39                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.31
 p-value of test no 40                 :    0.93
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.52
 p-value of test no 41                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.53
 p-value of test no 42                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 44                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.50
 p-value of test no 46                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.97
 p-value of test no 47                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.17
 p-value of test no 48                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.70
 p-value of test no 50                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   74.95
 p-value of test no 51                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   66.50
 p-value of test no 52                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.37
 p-value of test no 53                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  226.20
 p-value of test no 54                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  406.03
 p-value of test no 55                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1376.86
 p-value of test no 56                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7104.97
 p-value of test no 57                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 58                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 60                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.51
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 62                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 63                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 64                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.05
 p-value of test no 65                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    9.07
 p-value of test no 66                 :    0.11
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   99.34
 p-value of test no 67                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5110.66
 p-value of test no 68                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:43.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46065
 p-value of test no 70                 :    0.19
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870065
   j =  1                              :        399907877
   j =  2                              :            46051
   j =  3                              :                7
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46059
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870059
   j =  1                              :        399907882
   j =  2                              :            46059
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 74                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.034
 p-value of test no 77                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 78                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 81                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 83                 :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 84                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 85                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 88                 :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 90                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 91                 :    0.69
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 92                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 93                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.45
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 97                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.28
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 99                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 100                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 102                :    0.9945
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 104                :    0.36
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 105                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 107                :    0.78
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
 p-value of test no 109                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
 p-value of test no 110                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 111                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
 p-value of test no 112                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
 p-value of test no 113                :    0.92
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 114                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.05
 p-value of test no 115                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.04
 p-value of test no 116                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :  -0.053
 p-value of test no 117                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.28
 p-value of test no 118                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   52.61
 p-value of test no 119                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.43
 p-value of test no 120                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.95
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.41
 p-value of test no 122                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.69
 p-value of test no 123                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.50
 p-value of test no 124                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.63
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 126                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.61
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 128                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   35.73
 p-value of test no 129                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 130                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 131                :    0.11
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 132                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.65
 p-value of test no 133                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.81
 p-value of test no 134                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.43
 p-value of test no 135                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.07
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.19
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 138                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 139                :    0.24
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 140                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  152.52
 p-value of test no 141                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 143                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 144                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17376.96
 p-value of test no 145                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   24.85
 p-value of test no 146                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   43.82
 p-value of test no 147                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   12.65
 p-value of test no 148                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.75
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    9.41
 p-value of test no 150                :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.69
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.56
 p-value of test no 152                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   10.74
 p-value of test no 153                :    0.9941
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   14.15
 p-value of test no 154                :    0.94
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.99
 p-value of test no 155                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  172.16
 p-value of test no 156                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.30
 p-value of test no 157                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  499.33
 p-value of test no 158                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  114.90
 p-value of test no 159                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.00
 p-value of test no 160                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.36
 p-value of test no 161                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.54
 p-value of test no 162                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  465.01
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.18
 p-value of test no 164                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.24
 p-value of test no 165                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  328.86
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.11
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4956.59
 p-value of test no 168                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.04
 p-value of test no 169                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  227.32
 p-value of test no 170                :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  439.31
 p-value of test no 171                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.88
 p-value of test no 172                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4863.82
 p-value of test no 173                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.02
 p-value of test no 174                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.98
 p-value of test no 175                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.79
 p-value of test no 176                :    0.12
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.16
 p-value of test no 177                :    0.88
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.26
 p-value of test no 178                :    0.18
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.092
 p-value of test no 179                :    0.46
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.41
 p-value of test no 180                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
 p-value of test no 181                :    0.9945
 
 Anderson-Darling statistic = A2       :    2.69
 p-value of test no 182                :    0.04
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.13
 p-value of test no 183                :    0.98
 
 Sample variance                       :    1.41
 p-value of test no 184                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 186                :    0.25
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 187                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.48
 p-value of test no 188                :    0.31
 
 Sample variance                       :    0.92
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:23.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
 p-value of test no 190                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.12
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.015
 p-value of test no 193                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.23
 p-value of test no 196                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.03
 p-value of test no 198                :    0.75
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 201                :    0.87
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 202                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  171.21
 p-value of test no 203                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 204                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 206                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.19
 p-value of test no 207                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
 p-value of test no 208                :    0.9951
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 209                :    0.14
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 210                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10273.17
 p-value of test no 211                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 212                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 213                :    0.45
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 214                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.11
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.59
 p-value of test no 216                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 218                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 221                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4940.70
 p-value of test no 222                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4878.17
 p-value of test no 226                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3988.45
 p-value of test no 227                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4209.34
 p-value of test no 228                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11862.37
 p-value of test no 229                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.73
 p-value of test no 230                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.17
 p-value of test no 231                :    0.66
 
 
 -----------------------------------------------
 Total number of bits:  7999964046
 
 Normal statistic for number of bits   :   -0.28
 p-value of test no 232                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.95
 p-value of test no 233                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  8000114490
 
 Normal statistic for number of bits   :    0.91
 p-value of test no 234                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 235                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 236                :    0.18
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 237                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 238                :    0.41
 
 Sample variance                       :    0.45
 p-value of test no 239                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    1.48
 p-value of test no 242                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.62
 p-value of test no 243                :    0.73
 
 Sample variance                       :    2.34
 p-value of test no 244                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 245                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.48
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 247                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.81
 p-value of test no 249                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 251                :    0.31
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 252                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 253                :    0.42
 
 Sample variance                       :    0.46
 p-value of test no 254                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.11
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:15.42
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35979
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 3                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1388
 p-value of test no 8                  :    0.26
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334508
   j =  1                              :        599997224
   j =  2                              :             1388
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 10                 :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 11                 :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 12                 :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:53.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5467
 p-value of test no 13                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 14                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7201
 p-value of test no 15                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4240
 p-value of test no 16                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4241
 p-value of test no 17                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7349
 p-value of test no 18                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7145
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7306
 p-value of test no 20                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7242
 p-value of test no 21                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 22                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.46
 p-value of test no 23                 :    0.19
 
 Test on the Nm values of W_{n,i}(mNP1):    0.44
 p-value of test no 24                 :    0.81
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     920
 p-value of test no 25                 :    0.26
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 26                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    1.04
 p-value of test no 27                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.63
 p-value of test no 28                 :    0.15
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 29                 :    0.80
 
 Test on the Nm values of W_{n,i}(mNP1):    0.87
 p-value of test no 30                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     587
 p-value of test no 31                 :    0.69
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 32                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 34                 :    0.71
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.53
 p-value of test no 35                 :    0.71
 
 Test on the Nm values of W_{n,i}(mNP1):    1.15
 p-value of test no 36                 :    0.29
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     324
 p-value of test no 37                 :    0.09
 
 Stat. AD (mNP2)                       :    1.46
 p-value of test no 38                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.35
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.13
 p-value of test no 40                 :    0.29
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.09
 p-value of test no 41                 :    0.31
 
 Test on the Nm values of W_{n,i}(mNP1):    1.39
 p-value of test no 42                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     169
 p-value of test no 43                 :    0.07
 
 Stat. AD (mNP2)                       :    1.64
 p-value of test no 44                 :    0.15
 
 Stat. AD after spacings (mNP2-S)      :    1.38
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.24
 p-value of test no 46                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   21.26
 p-value of test no 47                 :  3.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.48
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   35.32
 p-value of test no 49                 :  8.6e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.63
 p-value of test no 50                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.88
 p-value of test no 51                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.35
 p-value of test no 52                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.61
 p-value of test no 53                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  254.63
 p-value of test no 54                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  440.65
 p-value of test no 55                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.51
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7052.87
 p-value of test no 57                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 60                 :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.32
 p-value of test no 61                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.43
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 64                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.69
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.77
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  105.27
 p-value of test no 67                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.61
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:44.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45886
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869886
   j =  1                              :        399908236
   j =  2                              :            45870
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45836
 p-value of test no 71                 :    0.58
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869836
   j =  1                              :        399908330
   j =  2                              :            45832
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 73                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 74                 :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.74
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 76                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 77                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 78                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.075
 p-value of test no 79                 :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.48
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 81                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 83                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 84                 :    0.69
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 86                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 87                 :    0.88
 
 Anderson-Darling statistic = A2       :    2.41
 p-value of test no 88                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.97
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 90                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 92                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 93                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 99                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 100                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.023
 p-value of test no 101                :    0.94
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 102                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 103                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.27
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 105                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 106                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 107                :    0.91
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 108                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
 p-value of test no 109                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
 p-value of test no 110                :    0.97
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 111                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
 p-value of test no 112                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
 p-value of test no 113                :    0.32
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.38
 p-value of test no 115                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.78
 p-value of test no 116                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.57
 p-value of test no 117                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.72
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.56
 p-value of test no 119                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:23.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.21
 p-value of test no 120                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.22
 p-value of test no 121                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.03
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.62
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.57
 p-value of test no 124                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   20.92
 p-value of test no 125                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 126                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 127                :    0.11
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 128                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.76
 p-value of test no 129                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 130                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 132                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.96
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.64
 p-value of test no 134                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.28
 p-value of test no 135                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.63
 p-value of test no 136                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.73
 p-value of test no 137                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 138                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 139                :    0.82
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 140                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  105.34
 p-value of test no 141                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 143                :    0.54
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 144                :    0.88
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17539.90
 p-value of test no 145                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.51
 p-value of test no 146                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.37
 p-value of test no 147                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.52
 p-value of test no 148                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.35
 p-value of test no 149                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.97
 p-value of test no 150                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.89
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   26.93
 p-value of test no 152                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.53
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.59
 p-value of test no 154                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.01
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.90
 p-value of test no 156                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  113.23
 p-value of test no 157                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  473.59
 p-value of test no 158                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.89
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.23
 p-value of test no 160                :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.55
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.97
 p-value of test no 162                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  543.48
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  199.06
 p-value of test no 164                :  3.5e-4    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   79.58
 p-value of test no 165                :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  346.62
 p-value of test no 166                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  377.15
 p-value of test no 167                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5025.25
 p-value of test no 168                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  341.22
 p-value of test no 169                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  187.58
 p-value of test no 170                :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  420.79
 p-value of test no 171                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  349.60
 p-value of test no 172                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4861.02
 p-value of test no 173                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.27
 p-value of test no 174                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.19
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.72
 p-value of test no 176                :    0.16
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 177                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.38
 p-value of test no 178                :    0.90
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 179                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 180                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 181                :    0.04
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 182                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.20
 p-value of test no 183                :    0.12
 
 Sample variance                       :    1.18
 p-value of test no 184                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.18
 p-value of test no 187                :    0.9952
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.18
 p-value of test no 188                :    0.57
 
 Sample variance                       :    0.86
 p-value of test no 189                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
 p-value of test no 190                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 191                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 192                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 195                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.45
 p-value of test no 196                :    0.81
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 197                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.68
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.68
 
 Anderson-Darling statistic = A2       :    0.15
 p-value of test no 202                :    0.9985
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  199.09
 p-value of test no 203                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 204                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 206                :    0.91
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.30
 p-value of test no 207                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 208                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 210                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10052.52
 p-value of test no 211                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 213                :    0.64
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 214                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10047.89
 p-value of test no 215                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.19
 p-value of test no 216                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 217                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.77
 p-value of test no 218                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 220                :    0.48
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4879.78
 p-value of test no 222                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 223                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 224                :    0.37
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 225                :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4923.90
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4118.45
 p-value of test no 227                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4116.06
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.46
 p-value of test no 229                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11704.89
 p-value of test no 230                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.30
 p-value of test no 231                :    0.35
 
 
 -----------------------------------------------
 Total number of bits:  8000073693
 
 Normal statistic for number of bits   :    0.58
 p-value of test no 232                :    0.28
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   44.54
 p-value of test no 233                :    0.82
 
 
 -----------------------------------------------
 Total number of bits:  7999886283
 
 Normal statistic for number of bits   :   -0.90
 p-value of test no 234                :    0.82
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 235                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 236                :    0.42
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 237                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.091
 p-value of test no 238                :    0.46
 
 Sample variance                       :    0.50
 p-value of test no 239                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 241                :    0.43
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 242                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.12
 p-value of test no 243                :    0.55
 
 Sample variance                       :    1.35
 p-value of test no 244                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 246                :    0.40
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.25
 p-value of test no 248                :    0.40
 
 Sample variance                       :    0.93
 p-value of test no 249                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 251                :    0.10
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 252                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.81
 p-value of test no 254                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:51.37
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  77  RandomWalk1 R (L=1000, r=20)    3.5e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35980
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.9959
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 3                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1375
 p-value of test no 4                  :    0.39
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334495
   j =  1                              :        599997250
   j =  2                              :             1375
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:18.24
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 5                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 6                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:20.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1411
 p-value of test no 7                  :    0.11
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334531
   j =  1                              :        599997178
   j =  2                              :             1411
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1419
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334539
   j =  1                              :        599997162
   j =  2                              :             1419
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1352
 p-value of test no 9                  :    0.62
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334472
   j =  1                              :        599997296
   j =  2                              :             1352
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 12                 :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5395
 p-value of test no 13                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 14                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7479
 p-value of test no 15                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4313
 p-value of test no 17                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7315
 p-value of test no 18                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7432
 p-value of test no 19                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7208
 p-value of test no 20                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7367
 p-value of test no 21                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.80
 p-value of test no 22                 :    0.12
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 23                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 24                 :    0.53
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     868
 p-value of test no 25                 :    0.85
 
 Stat. AD (mNP2)                       :    3.90
 p-value of test no 26                 :  9.7e-3
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.58
 p-value of test no 28                 :    0.16
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    2.73
 p-value of test no 30                 :    0.04
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     632
 p-value of test no 31                 :    0.10
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 32                 :    0.76
 
 Stat. AD after spacings (mNP2-S)      :    0.42
 p-value of test no 33                 :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 34                 :    0.40
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.69
 p-value of test no 35                 :    0.56
 
 Test on the Nm values of W_{n,i}(mNP1):    0.96
 p-value of test no 36                 :    0.38
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 40                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.49
 p-value of test no 41                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    1.70
 p-value of test no 42                 :    0.14
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     175
 p-value of test no 43                 :    0.02
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 44                 :    0.92
 
 Stat. AD after spacings (mNP2-S)      :    0.27
 p-value of test no 45                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.61
 p-value of test no 46                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.11
 p-value of test no 47                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.59
 p-value of test no 48                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.43
 p-value of test no 49                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   47.00
 p-value of test no 50                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.21
 p-value of test no 51                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.74
 p-value of test no 52                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.99
 p-value of test no 53                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  249.10
 p-value of test no 54                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  410.43
 p-value of test no 55                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1397.61
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7024.10
 p-value of test no 57                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 59                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 60                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.61
 p-value of test no 61                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 62                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 64                 :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   63.30
 p-value of test no 65                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.79
 p-value of test no 66                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  136.88
 p-value of test no 67                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5194.17
 p-value of test no 68                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45852
 p-value of test no 70                 :    0.55
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869852
   j =  1                              :        399908302
   j =  2                              :            45840
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45795
 p-value of test no 71                 :    0.65
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869795
   j =  1                              :        399908412
   j =  2                              :            45791
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 72                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 73                 :    0.55
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 74                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 76                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 78                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 79                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.030
 p-value of test no 80                 :    0.93
 
 Anderson-Darling statistic = A2       :    3.19
 p-value of test no 81                 :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9915
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 84                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 86                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.28
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 88                 :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.83
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 91                 :    0.98
 
 Anderson-Darling statistic = A2       :    3.31
 p-value of test no 92                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 93                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 95                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 97                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 99                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 100                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.33
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 102                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 103                :  3.7e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 104                :    0.96
 
 Anderson-Darling statistic = A2       :    4.96
 p-value of test no 105                :  3.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 107                :    0.70
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 108                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 111                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
 p-value of test no 112                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
 p-value of test no 113                :    0.57
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 114                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 115                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    2.63
 p-value of test no 116                :  4.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.67
 p-value of test no 117                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.81
 p-value of test no 118                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.80
 p-value of test no 119                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.23
 p-value of test no 120                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.59
 p-value of test no 121                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.08
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.53
 p-value of test no 123                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.27
 p-value of test no 124                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.99
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.091
 p-value of test no 126                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  1.0e-2
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 128                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.77
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 130                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 132                :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   29.66
 p-value of test no 133                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.88
 p-value of test no 134                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.38
 p-value of test no 135                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 136                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 138                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 139                :    0.39
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 140                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  122.85
 p-value of test no 141                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 142                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 143                :  7.9e-3
 
 Anderson-Darling statistic = A2       :    3.58
 p-value of test no 144                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17904.35
 p-value of test no 145                :  5.8e-3
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   44.41
 p-value of test no 146                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.77
 p-value of test no 147                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.72
 p-value of test no 148                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   21.44
 p-value of test no 149                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.46
 p-value of test no 150                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.67
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   23.43
 p-value of test no 152                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.86
 p-value of test no 153                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.24
 p-value of test no 154                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.18
 p-value of test no 155                :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  170.37
 p-value of test no 156                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.75
 p-value of test no 157                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.00
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  118.83
 p-value of test no 159                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.90
 p-value of test no 160                :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.48
 p-value of test no 161                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.21
 p-value of test no 162                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  507.61
 p-value of test no 163                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.95
 p-value of test no 164                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.03
 p-value of test no 165                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.49
 p-value of test no 166                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  413.05
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5008.07
 p-value of test no 168                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  394.13
 p-value of test no 169                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.67
 p-value of test no 170                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  407.34
 p-value of test no 171                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  435.41
 p-value of test no 172                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4932.60
 p-value of test no 173                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  377.12
 p-value of test no 174                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.10
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.71
 p-value of test no 176                :    0.39
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 177                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   25.16
 p-value of test no 178                :    0.01
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.73
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 181                :    0.14
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 182                :    0.31
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.89
 p-value of test no 183                :    0.19
 
 Sample variance                       :    1.50
 p-value of test no 184                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 186                :    0.30
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 187                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.82
 p-value of test no 188                :    0.21
 
 Sample variance                       :    0.91
 p-value of test no 189                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
 p-value of test no 190                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 192                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
 p-value of test no 193                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 194                :    0.25
 
 Anderson-Darling statistic = A2       :    1.00
 p-value of test no 195                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.40
 p-value of test no 198                :    0.60
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 200                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 201                :  4.3e-3
 
 Anderson-Darling statistic = A2       :    3.78
 p-value of test no 202                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  245.51
 p-value of test no 203                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 3.89e-3
 p-value of test no 205                :    0.9960
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 206                :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  164.55
 p-value of test no 207                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 208                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.33
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 210                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10074.68
 p-value of test no 211                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 212                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 214                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10268.54
 p-value of test no 215                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.22
 p-value of test no 216                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.71
 p-value of test no 217                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.85
 p-value of test no 218                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.72
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4866.89
 p-value of test no 222                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 224                :    0.93
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 225                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4776.06
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4085.35
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4194.38
 p-value of test no 228                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12004.42
 p-value of test no 229                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11971.58
 p-value of test no 230                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.77
 p-value of test no 231                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999930572
 
 Normal statistic for number of bits   :   -0.55
 p-value of test no 232                :    0.71
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.93
 p-value of test no 233                :    0.63
 
 
 -----------------------------------------------
 Total number of bits:  8000004777
 
 Normal statistic for number of bits   :   0.038
 p-value of test no 234                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 235                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    2.50
 p-value of test no 237                :    0.05
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.00
 p-value of test no 238                :    0.84
 
 Sample variance                       :    2.84
 p-value of test no 239                :  2.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 240                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 241                :    0.09
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 242                :    0.30
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.54
 p-value of test no 243                :    0.30
 
 Sample variance                       :    1.65
 p-value of test no 244                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.65
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.69
 p-value of test no 248                :    0.76
 
 Sample variance                       :    1.47
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 250                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.28
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 252                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.36
 p-value of test no 253                :    0.36
 
 Sample variance                       :    0.70
 p-value of test no 254                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:27.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35981
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 3                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:49.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 4                  :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 5                  :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 6                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:23.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1324
 p-value of test no 7                  :    0.86
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334444
   j =  1                              :        599997352
   j =  2                              :             1324
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1327
 p-value of test no 8                  :    0.84
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334447
   j =  1                              :        599997346
   j =  2                              :             1327
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 9                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1364
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334484
   j =  1                              :        599997272
   j =  2                              :             1364
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 12                 :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5508
 p-value of test no 13                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4339
 p-value of test no 14                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7288
 p-value of test no 15                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4304
 p-value of test no 16                 :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4468
 p-value of test no 17                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7269
 p-value of test no 18                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 20                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7266
 p-value of test no 21                 :    0.73
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 22                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.45
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 24                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     910
 p-value of test no 25                 :    0.37
 
 Stat. AD (mNP2)                       :    1.12
 p-value of test no 26                 :    0.30
 
 Stat. AD after spacings (mNP2-S)      :    0.94
 p-value of test no 27                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.53
 p-value of test no 28                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.19
 p-value of test no 29                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    1.43
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 32                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    2.52
 p-value of test no 33                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.24
 p-value of test no 34                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 35                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    1.03
 p-value of test no 36                 :    0.34
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     309
 p-value of test no 37                 :    0.31
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 38                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    1.52
 p-value of test no 39                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:09.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.29
 p-value of test no 41                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.59
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 44                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    0.47
 p-value of test no 45                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.30
 p-value of test no 46                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.16
 p-value of test no 47                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.18
 p-value of test no 48                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.76
 p-value of test no 49                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.66
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.09
 p-value of test no 51                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.34
 p-value of test no 52                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.50
 p-value of test no 53                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  222.86
 p-value of test no 54                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.84
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1316.98
 p-value of test no 56                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6912.97
 p-value of test no 57                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 59                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 60                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.25
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 62                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 63                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 64                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   87.87
 p-value of test no 65                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.49
 p-value of test no 66                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.53
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5059.00
 p-value of test no 68                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45545
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869545
   j =  1                              :        399908914
   j =  2                              :            45537
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46122
 p-value of test no 71                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870122
   j =  1                              :        399907758
   j =  2                              :            46118
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 72                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 73                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 74                 :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.82
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 76                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 77                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 78                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 79                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 80                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 81                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.033
 p-value of test no 84                 :    0.92
 
 Anderson-Darling statistic = A2       :    2.35
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 86                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 87                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 88                 :    0.9973
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 90                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 91                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 92                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 94                 :    0.63
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 95                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.72
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 97                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 98                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 99                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 100                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.32
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 102                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 103                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 104                :    0.86
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 105                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 107                :    0.34
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
 p-value of test no 110                :    0.25
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 111                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.95e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
 p-value of test no 113                :    0.22
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 114                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 115                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.65
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.48
 p-value of test no 117                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.35
 p-value of test no 118                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   45.30
 p-value of test no 119                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   60.97
 p-value of test no 120                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.32
 p-value of test no 121                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.14
 p-value of test no 122                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.46
 p-value of test no 123                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.42
 p-value of test no 124                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.85
 p-value of test no 125                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 126                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 127                :    0.38
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   51.49
 p-value of test no 129                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 130                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 131                :    0.56
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.70
 p-value of test no 133                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.00
 p-value of test no 134                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 135                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.080
 p-value of test no 136                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.50
 p-value of test no 137                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.051
 p-value of test no 139                :    0.92
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.99
 p-value of test no 141                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 142                :    0.68
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 143                :    0.50
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17456.73
 p-value of test no 145                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   52.86
 p-value of test no 146                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.76
 p-value of test no 147                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.63
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.34
 p-value of test no 149                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.15
 p-value of test no 150                :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   34.74
 p-value of test no 151                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.71
 p-value of test no 152                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   36.22
 p-value of test no 153                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   30.76
 p-value of test no 154                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.91
 p-value of test no 155                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:35.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.63
 p-value of test no 156                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.78
 p-value of test no 157                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  493.94
 p-value of test no 158                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  164.95
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.68
 p-value of test no 160                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:39.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.83
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.65
 p-value of test no 162                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  488.39
 p-value of test no 163                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  139.81
 p-value of test no 164                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   96.42
 p-value of test no 165                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.27
 p-value of test no 166                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  359.62
 p-value of test no 167                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5041.91
 p-value of test no 168                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  375.07
 p-value of test no 169                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.73
 p-value of test no 170                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  418.23
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  393.68
 p-value of test no 172                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.24
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  426.12
 p-value of test no 174                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.37
 p-value of test no 175                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.95
 p-value of test no 176                :    0.53
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.98
 p-value of test no 177                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.54
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.11
 p-value of test no 179                :    0.54
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.62
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 183                :    0.83
 
 Sample variance                       :    0.78
 p-value of test no 184                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 186                :    0.83
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 187                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.60
 p-value of test no 188                :    0.72
 
 Sample variance                       :    1.78
 p-value of test no 189                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
 p-value of test no 190                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.38
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 192                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
 p-value of test no 194                :    0.64
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 195                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.13
 p-value of test no 196                :    0.26
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.09
 p-value of test no 198                :    0.42
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  195.57
 p-value of test no 203                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 204                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
 p-value of test no 205                :    0.9911
 
 Anderson-Darling statistic = A2       :    3.67
 p-value of test no 206                :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  149.54
 p-value of test no 207                :    0.9969
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 209                :    0.69
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 210                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.72
 p-value of test no 211                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 212                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    1.12
 p-value of test no 214                :    0.30
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9927.20
 p-value of test no 215                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.40
 p-value of test no 216                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 217                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.82
 p-value of test no 218                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 219                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 220                :    0.67
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 221                :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4802.34
 p-value of test no 222                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 223                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 224                :    0.49
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 225                :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4993.97
 p-value of test no 226                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3953.27
 p-value of test no 227                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4152.50
 p-value of test no 228                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11951.48
 p-value of test no 229                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11777.25
 p-value of test no 230                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.32
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  7999924515
 
 Normal statistic for number of bits   :   -0.60
 p-value of test no 232                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.32
 p-value of test no 233                :    0.29
 
 
 -----------------------------------------------
 Total number of bits:  7999985142
 
 Normal statistic for number of bits   :   -0.12
 p-value of test no 234                :    0.55
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.040
 p-value of test no 235                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 236                :    0.03
 
 Anderson-Darling statistic = A2       :    3.44
 p-value of test no 237                :    0.02
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.42
 p-value of test no 238                :  7.7e-3
 
 Sample variance                       :    0.71
 p-value of test no 239                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 240                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 241                :    0.21
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 242                :    0.29
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.25
 p-value of test no 243                :    0.11
 
 Sample variance                       :    1.41
 p-value of test no 244                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 246                :    0.58
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 247                :    0.49
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.22
 p-value of test no 248                :    0.59
 
 Sample variance                       :    1.54
 p-value of test no 249                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 250                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 251                :    0.41
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 252                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.27
 p-value of test no 253                :    0.61
 
 Sample variance                       :    0.40
 p-value of test no 254                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:19.78
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35982
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 3                  :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 4                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 5                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:52.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1325
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334445
   j =  1                              :        599997350
   j =  2                              :             1325
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:24.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 7                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 8                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:14.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 9                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1343
 p-value of test no 10                 :    0.71
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334463
   j =  1                              :        599997314
   j =  2                              :             1343
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1395
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334515
   j =  1                              :        599997210
   j =  2                              :             1395
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 12                 :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5374
 p-value of test no 13                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4421
 p-value of test no 14                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 15                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4346
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4325
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7199
 p-value of test no 18                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7235
 p-value of test no 19                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7356
 p-value of test no 20                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7174
 p-value of test no 21                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 22                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.79
 p-value of test no 23                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.38
 p-value of test no 24                 :    0.21
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     876
 p-value of test no 25                 :    0.78
 
 Stat. AD (mNP2)                       :    0.48
 p-value of test no 26                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.63
 p-value of test no 27                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.23
 p-value of test no 28                 :    0.25
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.25
 p-value of test no 29                 :    0.07
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 30                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     579
 p-value of test no 31                 :    0.80
 
 Stat. AD (mNP2)                       :    1.75
 p-value of test no 32                 :    0.13
 
 Stat. AD after spacings (mNP2-S)      :    0.63
 p-value of test no 33                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 34                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.99
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    1.64
 p-value of test no 36                 :    0.15
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     327
 p-value of test no 37                 :    0.06
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 38                 :    0.45
 
 Stat. AD after spacings (mNP2-S)      :    0.61
 p-value of test no 39                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.70
 p-value of test no 41                 :    0.01
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 42                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     156
 p-value of test no 43                 :    0.32
 
 Stat. AD (mNP2)                       :    0.60
 p-value of test no 44                 :    0.65
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 45                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   10.00
 p-value of test no 46                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.08
 p-value of test no 47                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.52
 p-value of test no 48                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.12
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.05
 p-value of test no 50                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   46.70
 p-value of test no 51                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.96
 p-value of test no 52                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.09
 p-value of test no 53                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  227.04
 p-value of test no 54                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  420.36
 p-value of test no 55                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1470.78
 p-value of test no 56                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7165.36
 p-value of test no 57                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.014
 p-value of test no 58                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.65
 p-value of test no 59                 :  7.1e-3
 
 Anderson-Darling statistic = A2       :    4.31
 p-value of test no 60                 :  6.7e-3
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   54.36
 p-value of test no 61                 :  4.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 62                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.30
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 64                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   77.02
 p-value of test no 65                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.41
 p-value of test no 66                 :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.19
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4844.52
 p-value of test no 68                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:47.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46125
 p-value of test no 70                 :    0.13
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870125
   j =  1                              :        399907752
   j =  2                              :            46121
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45897
 p-value of test no 71                 :    0.47
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869897
   j =  1                              :        399908210
   j =  2                              :            45889
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:39.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 72                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 74                 :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.078
 p-value of test no 76                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 77                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 78                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 80                 :    0.60
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 81                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.32
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 83                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 84                 :    0.82
 
 Anderson-Darling statistic = A2       :    1.33
 p-value of test no 85                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 86                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 87                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 88                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 90                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 91                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 92                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 93                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 94                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.28
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.041
 p-value of test no 97                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 99                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 100                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.39
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 102                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 103                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.51
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 106                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 107                :    0.50
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 108                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
 p-value of test no 110                :    0.80
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 111                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
 p-value of test no 112                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
 p-value of test no 113                :    0.97
 
 Anderson-Darling statistic = A2       :    1.95
 p-value of test no 114                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.83
 p-value of test no 115                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.05
 p-value of test no 116                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 117                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.34
 p-value of test no 118                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   80.88
 p-value of test no 119                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.30
 p-value of test no 120                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   71.12
 p-value of test no 121                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.08
 p-value of test no 122                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.28
 p-value of test no 123                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.86
 p-value of test no 124                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   26.61
 p-value of test no 125                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 126                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.46
 p-value of test no 127                :  9.8e-3
 
 Anderson-Darling statistic = A2       :    3.47
 p-value of test no 128                :    0.02
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.59
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 130                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.49
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 132                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.57
 p-value of test no 133                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   15.93
 p-value of test no 134                :  1.2e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.25
 p-value of test no 135                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:13.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.14
 p-value of test no 137                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 139                :    0.79
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 140                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  117.74
 p-value of test no 141                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 142                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    :    0.37
 p-value of test no 143                :    0.05
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 144                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17651.82
 p-value of test no 145                :    0.12
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   51.31
 p-value of test no 146                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.31
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   23.04
 p-value of test no 148                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.31
 p-value of test no 149                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 150                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.45
 p-value of test no 151                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.79
 p-value of test no 152                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   25.34
 p-value of test no 153                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.50
 p-value of test no 154                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.69
 p-value of test no 155                :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  121.70
 p-value of test no 156                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.80
 p-value of test no 157                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  568.87
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.26
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.86
 p-value of test no 160                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  162.87
 p-value of test no 161                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  155.96
 p-value of test no 162                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  498.06
 p-value of test no 163                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  128.76
 p-value of test no 164                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.34
 p-value of test no 165                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.81
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  403.83
 p-value of test no 167                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.03
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  411.18
 p-value of test no 169                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.38
 p-value of test no 170                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  398.18
 p-value of test no 171                :    0.30
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  337.98
 p-value of test no 172                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5012.60
 p-value of test no 173                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.54
 p-value of test no 174                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  205.77
 p-value of test no 175                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   12.12
 p-value of test no 176                :    0.44
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.95
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.12
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.53
 p-value of test no 179                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 182                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.36
 p-value of test no 184                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 185                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 186                :    0.87
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 187                :    0.94
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 188                :    0.67
 
 Sample variance                       :    0.74
 p-value of test no 189                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 190                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
 p-value of test no 191                :    0.81
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 192                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
 p-value of test no 194                :    0.60
 
 Anderson-Darling statistic = A2       :    0.21
 p-value of test no 195                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.57
 p-value of test no 196                :    0.70
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 197                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.92
 p-value of test no 198                :    0.44
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 200                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.26
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 202                :    0.63
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.60
 p-value of test no 203                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.39
 p-value of test no 204                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.077
 p-value of test no 205                :    0.85
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 206                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  162.22
 p-value of test no 207                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 208                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 209                :    0.18
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 210                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10136.08
 p-value of test no 211                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 212                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.39
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 214                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.55
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.031
 p-value of test no 216                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.15
 p-value of test no 217                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.54
 p-value of test no 218                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 219                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 220                :    0.73
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 221                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4806.14
 p-value of test no 222                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 223                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.02
 p-value of test no 225                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4788.08
 p-value of test no 226                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3999.32
 p-value of test no 227                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4117.18
 p-value of test no 228                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11772.80
 p-value of test no 229                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11820.06
 p-value of test no 230                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   84.86
 p-value of test no 231                :  4.6e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999870899
 
 Normal statistic for number of bits   :   -1.02
 p-value of test no 232                :    0.85
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.97
 p-value of test no 233                :    0.30
 
 
 -----------------------------------------------
 Total number of bits:  7999965774
 
 Normal statistic for number of bits   :   -0.27
 p-value of test no 234                :    0.61
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.10
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 237                :    0.25
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.72
 p-value of test no 238                :    0.24
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 241                :    0.33
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 242                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.19
 p-value of test no 243                :    0.42
 
 Sample variance                       :    0.93
 p-value of test no 244                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.29
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 247                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.39
 p-value of test no 248                :    0.65
 
 Sample variance                       :    2.18
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 250                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.53
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 252                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    0.98
 p-value of test no 254                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:20.43
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35983
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 3                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 4                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 5                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1404
 p-value of test no 6                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334524
   j =  1                              :        599997192
   j =  2                              :             1404
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:15.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 7                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1315
 p-value of test no 8                  :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334435
   j =  1                              :        599997370
   j =  2                              :             1315
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:12.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 9                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1287
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334407
   j =  1                              :        599997426
   j =  2                              :             1287
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1313
 p-value of test no 11                 :    0.92
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334433
   j =  1                              :        599997374
   j =  2                              :             1313
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 12                 :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5391
 p-value of test no 13                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 14                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 15                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4394
 p-value of test no 16                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4234
 p-value of test no 17                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7359
 p-value of test no 18                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7303
 p-value of test no 19                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7418
 p-value of test no 20                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7378
 p-value of test no 21                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.69
 p-value of test no 22                 :    0.56
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.89
 p-value of test no 23                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    2.02
 p-value of test no 24                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 26                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    3.45
 p-value of test no 27                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.17
 p-value of test no 28                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.65
 p-value of test no 29                 :    0.60
 
 Test on the Nm values of W_{n,i}(mNP1):    1.20
 p-value of test no 30                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     598
 p-value of test no 31                 :    0.52
 
 Stat. AD (mNP2)                       :    0.51
 p-value of test no 32                 :    0.73
 
 Stat. AD after spacings (mNP2-S)      :    0.93
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.97
 p-value of test no 34                 :    0.37
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    3.12
 p-value of test no 35                 :    0.02
 
 Test on the Nm values of W_{n,i}(mNP1):    0.88
 p-value of test no 36                 :    0.43
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.53
 p-value of test no 38                 :    0.72
 
 Stat. AD after spacings (mNP2-S)      :    0.88
 p-value of test no 39                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.28
 p-value of test no 40                 :    0.02
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.73
 
 Test on the Nm values of W_{n,i}(mNP1):    1.09
 p-value of test no 42                 :    0.31
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     165
 p-value of test no 43                 :    0.12
 
 Stat. AD (mNP2)                       :    2.24
 p-value of test no 44                 :    0.07
 
 Stat. AD after spacings (mNP2-S)      :    1.29
 p-value of test no 45                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.89
 p-value of test no 46                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.28
 p-value of test no 47                 :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.80
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   15.67
 p-value of test no 49                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.05
 p-value of test no 50                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.89
 p-value of test no 51                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   40.72
 p-value of test no 52                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.72
 p-value of test no 53                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  236.53
 p-value of test no 54                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  458.26
 p-value of test no 55                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1461.47
 p-value of test no 56                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7086.99
 p-value of test no 57                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 58                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 59                 :    0.42
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 60                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   28.46
 p-value of test no 61                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 63                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 64                 :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.75
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:13.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    7.97
 p-value of test no 66                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  132.35
 p-value of test no 67                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5189.04
 p-value of test no 68                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:48.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45932
 p-value of test no 70                 :    0.40
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869932
   j =  1                              :        399908142
   j =  2                              :            45920
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45968
 p-value of test no 71                 :    0.34
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869968
   j =  1                              :        399908068
   j =  2                              :            45960
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 72                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 73                 :    0.08
 
 Anderson-Darling statistic = A2       :    2.28
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 77                 :    0.97
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 78                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 79                 :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 80                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 81                 :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.57
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 84                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 85                 :    0.94
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 86                 :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 87                 :    0.79
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.91
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 92                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 93                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 94                 :    0.59
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 95                 :    0.37
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.67
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 100                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 101                :    0.57
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 102                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 103                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 104                :    0.25
 
 Anderson-Darling statistic = A2       :    1.15
 p-value of test no 105                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 106                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 107                :    0.98
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 108                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
 p-value of test no 109                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
 p-value of test no 110                :    0.51
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
 p-value of test no 113                :    0.17
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 114                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    1.10
 p-value of test no 115                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.62
 p-value of test no 116                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.92
 p-value of test no 118                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.71
 p-value of test no 119                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   54.64
 p-value of test no 120                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.62
 p-value of test no 121                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.26
 p-value of test no 122                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.25
 p-value of test no 123                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.03
 p-value of test no 124                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   15.55
 p-value of test no 125                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 126                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.74
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 128                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.70
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 131                :    0.62
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 132                :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   40.47
 p-value of test no 133                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.38
 p-value of test no 134                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.63
 p-value of test no 135                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 139                :    0.69
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 140                :    0.82
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  128.81
 p-value of test no 141                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 142                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 143                :    0.11
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 144                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.34
 p-value of test no 145                :    0.42
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.28
 p-value of test no 146                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   51.12
 p-value of test no 147                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.57
 p-value of test no 148                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.30
 p-value of test no 149                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.89
 p-value of test no 150                :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.93
 p-value of test no 151                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.49
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.92
 p-value of test no 153                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   28.06
 p-value of test no 154                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.18
 p-value of test no 155                :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.17
 p-value of test no 156                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.38
 p-value of test no 157                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  443.62
 p-value of test no 158                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  163.79
 p-value of test no 159                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   54.25
 p-value of test no 160                :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  111.88
 p-value of test no 161                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  106.79
 p-value of test no 162                :    0.9938
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.11
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.34
 p-value of test no 164                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   64.67
 p-value of test no 165                :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  316.26
 p-value of test no 166                :    0.9951
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  347.84
 p-value of test no 167                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5031.96
 p-value of test no 168                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  374.70
 p-value of test no 169                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.80
 p-value of test no 170                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  383.69
 p-value of test no 171                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  379.75
 p-value of test no 172                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5132.18
 p-value of test no 173                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  348.37
 p-value of test no 174                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.05
 p-value of test no 175                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.52
 p-value of test no 176                :    0.21
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.48
 p-value of test no 177                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.56
 p-value of test no 178                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.82
 p-value of test no 179                :    0.9976
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 180                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 181                :    0.68
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 182                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.20
 p-value of test no 183                :    0.58
 
 Sample variance                       :    1.09
 p-value of test no 184                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.54
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 187                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 188                :    0.37
 
 Sample variance                       :    0.55
 p-value of test no 189                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 191                :    0.36
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 192                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
 p-value of test no 194                :    0.51
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 195                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.53
 p-value of test no 196                :    0.59
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.32
 p-value of test no 198                :    0.61
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 201                :    0.71
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 202                :    0.59
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.85
 p-value of test no 203                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 204                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 205                :    0.89
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  183.92
 p-value of test no 207                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 209                :    0.35
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 210                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9933.38
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 213                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10024.68
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.49
 p-value of test no 216                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 217                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.87
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 220                :    0.77
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4832.74
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 224                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 225                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.42
 p-value of test no 226                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4307.93
 p-value of test no 227                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3907.28
 p-value of test no 228                :    0.9905
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11832.80
 p-value of test no 229                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12130.25
 p-value of test no 230                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   83.41
 p-value of test no 231                :  6.3e-3
 
 
 -----------------------------------------------
 Total number of bits:  7999978458
 
 Normal statistic for number of bits   :   -0.17
 p-value of test no 232                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   70.86
 p-value of test no 233                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000047824
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 235                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 236                :    0.78
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 237                :    0.50
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 238                :    0.79
 
 Sample variance                       :    0.60
 p-value of test no 239                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 241                :    0.16
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 242                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         : -9.80e-3
 p-value of test no 243                :    0.50
 
 Sample variance                       :    1.32
 p-value of test no 244                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 246                :    0.67
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 247                :    0.73
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 248                :    0.64
 
 Sample variance                       :    1.33
 p-value of test no 249                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 250                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 251                :    0.24
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 252                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.79
 p-value of test no 253                :    0.22
 
 Sample variance                       :    1.60
 p-value of test no 254                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.03
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:42:23.67
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35984
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 3                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 4                  :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:22.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 5                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1451
 p-value of test no 6                  :    0.01
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334571
   j =  1                              :        599997098
   j =  2                              :             1451
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1308
 p-value of test no 7                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334428
   j =  1                              :        599997384
   j =  2                              :             1308
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 8                  :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:13.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 9                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1384
 p-value of test no 10                 :    0.30
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334504
   j =  1                              :        599997232
   j =  2                              :             1384
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1341
 p-value of test no 11                 :    0.73
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334461
   j =  1                              :        599997318
   j =  2                              :             1341
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5333
 p-value of test no 13                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4350
 p-value of test no 14                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7292
 p-value of test no 15                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4289
 p-value of test no 16                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4400
 p-value of test no 17                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7205
 p-value of test no 18                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7259
 p-value of test no 19                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7343
 p-value of test no 20                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7250
 p-value of test no 21                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.04
 p-value of test no 22                 :    0.34
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.47
 p-value of test no 23                 :    0.78
 
 Test on the Nm values of W_{n,i}(mNP1):    0.22
 p-value of test no 24                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     909
 p-value of test no 25                 :    0.39
 
 Stat. AD (mNP2)                       :    0.99
 p-value of test no 26                 :    0.36
 
 Stat. AD after spacings (mNP2-S)      :    0.69
 p-value of test no 27                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 28                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.35
 p-value of test no 29                 :    0.22
 
 Test on the Nm values of W_{n,i}(mNP1):    1.29
 p-value of test no 30                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     571
 p-value of test no 31                 :    0.88
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 32                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 33                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.79
 p-value of test no 34                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.82
 
 Test on the Nm values of W_{n,i}(mNP1):    0.55
 p-value of test no 36                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     269
 p-value of test no 37                 :    0.96
 
 Stat. AD (mNP2)                       :    1.04
 p-value of test no 38                 :    0.34
 
 Stat. AD after spacings (mNP2-S)      :    0.78
 p-value of test no 39                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.86
 p-value of test no 40                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    1.19
 p-value of test no 42                 :    0.27
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     155
 p-value of test no 43                 :    0.35
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.38
 p-value of test no 45                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.44
 p-value of test no 46                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.59
 p-value of test no 47                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.97
 p-value of test no 48                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   18.88
 p-value of test no 49                 :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   83.52
 p-value of test no 50                 :  6.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.82
 p-value of test no 51                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.67
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.78
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  210.50
 p-value of test no 54                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  444.38
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1482.81
 p-value of test no 56                 :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6884.83
 p-value of test no 57                 :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 58                 :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 60                 :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.46
 p-value of test no 61                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 62                 :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 63                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 64                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.46
 p-value of test no 65                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.79
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  126.31
 p-value of test no 67                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5066.53
 p-value of test no 68                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:50.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45875
 p-value of test no 70                 :    0.51
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869875
   j =  1                              :        399908253
   j =  2                              :            45869
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46097
 p-value of test no 71                 :    0.16
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870097
   j =  1                              :        399907811
   j =  2                              :            46087
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 72                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 73                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.84
 p-value of test no 74                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.038
 p-value of test no 76                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 78                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
 p-value of test no 80                 :    0.9955
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 2.99e+6
 p-value of test no 82                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 84                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.97
 p-value of test no 85                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 86                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 88                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.06
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 90                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 91                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 92                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 93                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 94                 :    0.38
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 95                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.19
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 97                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 98                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 99                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 101                :    0.87
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 102                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 103                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.017
 p-value of test no 104                :    0.98
 
 Anderson-Darling statistic = A2       :    2.14
 p-value of test no 105                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 106                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 107                :    0.39
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 108                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
 p-value of test no 109                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    : 2.16e-5
 p-value of test no 110                :    0.98
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 111                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
 p-value of test no 112                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
 p-value of test no 113                :    0.85
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.31
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.37
 p-value of test no 116                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.44
 p-value of test no 117                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.83
 p-value of test no 118                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.31
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:26.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.84
 p-value of test no 120                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.07
 p-value of test no 121                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.57
 p-value of test no 122                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.51
 p-value of test no 123                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   30.83
 p-value of test no 124                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.14
 p-value of test no 125                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 127                :    0.49
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 128                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.37
 p-value of test no 129                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.037
 p-value of test no 130                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 132                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.42
 p-value of test no 133                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.91
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.02
 p-value of test no 135                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    5.19
 p-value of test no 136                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.69
 p-value of test no 137                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 138                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    1.65
 p-value of test no 140                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  107.04
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 142                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.071
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 144                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17335.87
 p-value of test no 145                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.78
 p-value of test no 146                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   39.92
 p-value of test no 147                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.12
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   25.83
 p-value of test no 149                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   22.93
 p-value of test no 150                :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.68
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   49.03
 p-value of test no 152                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.07
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.20
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.09
 p-value of test no 155                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.82
 p-value of test no 156                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.00
 p-value of test no 157                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  462.29
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.38
 p-value of test no 159                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.47
 p-value of test no 160                :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  132.04
 p-value of test no 161                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  166.82
 p-value of test no 162                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  494.76
 p-value of test no 163                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  148.57
 p-value of test no 164                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.88
 p-value of test no 165                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.80
 p-value of test no 166                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.84
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4958.49
 p-value of test no 168                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.43
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.18
 p-value of test no 170                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:32.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.12
 p-value of test no 171                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.44
 p-value of test no 172                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5146.90
 p-value of test no 173                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  430.59
 p-value of test no 174                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  172.94
 p-value of test no 175                :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.88
 p-value of test no 176                :    0.63
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.35
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.52
 p-value of test no 178                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 179                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 180                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.065
 p-value of test no 181                :    0.88
 
 Anderson-Darling statistic = A2       :    1.34
 p-value of test no 182                :    0.22
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 183                :    0.90
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 185                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 186                :    0.21
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 187                :    0.52
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.16
 p-value of test no 188                :    0.56
 
 Sample variance                       :    0.85
 p-value of test no 189                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
 p-value of test no 191                :    0.68
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
 p-value of test no 193                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.28
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 195                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.65
 p-value of test no 196                :    0.69
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.85
 p-value of test no 198                :    0.21
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 201                :    0.48
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 202                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.44
 p-value of test no 203                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 204                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.21
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 206                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  231.08
 p-value of test no 207                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 209                :    0.76
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 210                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.45
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 212                :    0.28
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.54
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9939.77
 p-value of test no 215                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 216                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.26
 p-value of test no 217                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.64
 p-value of test no 218                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 220                :    0.87
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 221                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4737.94
 p-value of test no 222                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 223                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 224                :    0.52
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 225                :    0.77
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4873.79
 p-value of test no 226                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4248.46
 p-value of test no 227                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3971.33
 p-value of test no 228                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.34
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11569.57
 p-value of test no 230                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.78
 p-value of test no 231                :    0.17
 
 
 -----------------------------------------------
 Total number of bits:  8000111706
 
 Normal statistic for number of bits   :    0.88
 p-value of test no 232                :    0.19
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.77
 p-value of test no 233                :    0.22
 
 
 -----------------------------------------------
 Total number of bits:  8000047695
 
 Normal statistic for number of bits   :    0.38
 p-value of test no 234                :    0.35
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 235                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.64
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 237                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 238                :    0.65
 
 Sample variance                       :    1.43
 p-value of test no 239                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 240                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 241                :    0.65
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 242                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.19
 p-value of test no 243                :    0.57
 
 Sample variance                       :    1.61
 p-value of test no 244                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 245                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 246                :    0.61
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 247                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    1.76
 p-value of test no 249                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 250                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 251                :    0.48
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 252                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.24
 p-value of test no 253                :    0.41
 
 Sample variance                       :    0.94
 p-value of test no 254                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:07.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35985
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1297
 p-value of test no 3                  :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334417
   j =  1                              :        599997406
   j =  2                              :             1297
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:02.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1303
 p-value of test no 4                  :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334423
   j =  1                              :        599997394
   j =  2                              :             1303
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1383
 p-value of test no 5                  :    0.31
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334503
   j =  1                              :        599997234
   j =  2                              :             1383
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 6                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1390
 p-value of test no 7                  :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334510
   j =  1                              :        599997220
   j =  2                              :             1390
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1362
 p-value of test no 8                  :    0.52
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334482
   j =  1                              :        599997276
   j =  2                              :             1362
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:11.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1369
 p-value of test no 9                  :    0.45
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334489
   j =  1                              :        599997262
   j =  2                              :             1369
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1302
 p-value of test no 10                 :    0.95
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334422
   j =  1                              :        599997396
   j =  2                              :             1302
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 11                 :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1444
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334564
   j =  1                              :        599997112
   j =  2                              :             1444
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5506
 p-value of test no 13                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4369
 p-value of test no 14                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7290
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4405
 p-value of test no 16                 :    0.15
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4266
 p-value of test no 17                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7420
 p-value of test no 19                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7471
 p-value of test no 20                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7525
 p-value of test no 21                 :  8.2e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.92
 p-value of test no 22                 :    0.10
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 23                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    0.28
 p-value of test no 24                 :    0.96
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     903
 p-value of test no 25                 :    0.46
 
 Stat. AD (mNP2)                       :    2.76
 p-value of test no 26                 :    0.04
 
 Stat. AD after spacings (mNP2-S)      :    1.74
 p-value of test no 27                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.50
 p-value of test no 28                 :    0.18
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 29                 :    0.85
 
 Test on the Nm values of W_{n,i}(mNP1):    0.75
 p-value of test no 30                 :    0.52
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     616
 p-value of test no 31                 :    0.26
 
 Stat. AD (mNP2)                       :    0.33
 p-value of test no 32                 :    0.91
 
 Stat. AD after spacings (mNP2-S)      :    0.82
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.64
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.92
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.24
 p-value of test no 36                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     295
 p-value of test no 37                 :    0.60
 
 Stat. AD (mNP2)                       :    0.86
 p-value of test no 38                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 39                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.11
 p-value of test no 40                 :    0.30
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 41                 :    0.43
 
 Test on the Nm values of W_{n,i}(mNP1):    0.23
 p-value of test no 42                 :    0.98
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 44                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.22
 p-value of test no 45                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.95
 p-value of test no 46                 :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   11.07
 p-value of test no 47                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.07
 p-value of test no 48                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   13.25
 p-value of test no 49                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   63.63
 p-value of test no 50                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.47
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.80
 p-value of test no 52                 :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.59
 p-value of test no 53                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  240.52
 p-value of test no 54                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  396.15
 p-value of test no 55                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1483.97
 p-value of test no 56                 :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6907.13
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 59                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 60                 :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   33.30
 p-value of test no 61                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 62                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.40
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 64                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.50
 p-value of test no 65                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    3.97
 p-value of test no 66                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  137.44
 p-value of test no 67                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.60
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9985
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45721
 p-value of test no 70                 :    0.77
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869721
   j =  1                              :        399908563
   j =  2                              :            45711
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45696
 p-value of test no 71                 :    0.80
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869696
   j =  1                              :        399908609
   j =  2                              :            45694
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 72                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 73                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 74                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.65
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 77                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 78                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 79                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 83                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 85                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 86                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 87                 :    0.45
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 88                 :    0.50
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.68
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.042
 p-value of test no 90                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 91                 :    0.20
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 92                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 93                 :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 94                 :    0.03
 
 Anderson-Darling statistic = A2       :    1.97
 p-value of test no 95                 :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 97                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 98                 :    0.67
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 99                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 100                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 101                :    0.92
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 102                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 104                :    0.07
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 105                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 106                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.15
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 108                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
 p-value of test no 109                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    2.76
 p-value of test no 111                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
 p-value of test no 112                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
 p-value of test no 113                :    0.45
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 114                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.23
 p-value of test no 115                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 116                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 117                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 118                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.17
 p-value of test no 119                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.93
 p-value of test no 120                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.56
 p-value of test no 121                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.15
 p-value of test no 122                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.31
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   45.52
 p-value of test no 124                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   30.87
 p-value of test no 125                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 126                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 127                :    0.77
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 128                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.93
 p-value of test no 129                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 131                :    0.47
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 132                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.25
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.31
 p-value of test no 134                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.95
 p-value of test no 135                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.05
 p-value of test no 136                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.36
 p-value of test no 137                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 138                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.042
 p-value of test no 139                :    0.94
 
 Anderson-Darling statistic = A2       :    1.30
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  106.85
 p-value of test no 141                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 142                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    2.09
 p-value of test no 144                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17796.87
 p-value of test no 145                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.48
 p-value of test no 146                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   35.15
 p-value of test no 147                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.38
 p-value of test no 148                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   20.81
 p-value of test no 149                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.43
 p-value of test no 150                :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.78
 p-value of test no 151                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.29
 p-value of test no 152                :    0.36
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   31.51
 p-value of test no 153                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   36.35
 p-value of test no 154                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.62
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.46
 p-value of test no 156                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.15
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  484.02
 p-value of test no 158                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.21
 p-value of test no 159                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :  102.80
 p-value of test no 160                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.46
 p-value of test no 161                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  124.90
 p-value of test no 162                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.49
 p-value of test no 163                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.72
 p-value of test no 164                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.36
 p-value of test no 165                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  350.80
 p-value of test no 166                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  380.74
 p-value of test no 167                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4960.62
 p-value of test no 168                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  385.03
 p-value of test no 169                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  200.38
 p-value of test no 170                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  354.99
 p-value of test no 171                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.66
 p-value of test no 172                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4953.75
 p-value of test no 173                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  395.22
 p-value of test no 174                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  157.49
 p-value of test no 175                :    0.99
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.20
 p-value of test no 176                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.08
 p-value of test no 178                :    0.78
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.94
 p-value of test no 179                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.71
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 182                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.02
 p-value of test no 183                :    0.85
 
 Sample variance                       :    0.45
 p-value of test no 184                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 185                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 187                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    1.33
 p-value of test no 189                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
 p-value of test no 190                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 192                :    0.9922
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
 p-value of test no 193                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.21
 p-value of test no 196                :    0.32
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    8.46
 p-value of test no 198                :    0.39
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 200                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 201                :    0.15
 
 Anderson-Darling statistic = A2       :    1.14
 p-value of test no 202                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  224.83
 p-value of test no 203                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 204                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 205                :    0.56
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 206                :    0.38
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.11
 p-value of test no 207                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.48
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 210                :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9975.22
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 212                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 214                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9964.48
 p-value of test no 215                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.10
 p-value of test no 216                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.58
 p-value of test no 217                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.07
 p-value of test no 218                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 221                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4976.46
 p-value of test no 222                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 224                :    0.86
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4822.35
 p-value of test no 226                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.03
 p-value of test no 227                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4239.62
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11645.21
 p-value of test no 229                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11916.52
 p-value of test no 230                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.45
 p-value of test no 231                :    0.50
 
 
 -----------------------------------------------
 Total number of bits:  8000177901
 
 Normal statistic for number of bits   :    1.41
 p-value of test no 232                :    0.08
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.97
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  8000015079
 
 Normal statistic for number of bits   :    0.12
 p-value of test no 234                :    0.45
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 235                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 236                :    0.63
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 237                :    0.71
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 238                :    0.64
 
 Sample variance                       :    0.47
 p-value of test no 239                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 240                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.26
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 242                :    0.37
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 243                :    0.14
 
 Sample variance                       :    1.10
 p-value of test no 244                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 245                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 246                :    0.81
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 247                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 248                :    0.55
 
 Sample variance                       :    1.00
 p-value of test no 249                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 250                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 251                :    0.49
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 252                :    0.70
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.10
 p-value of test no 253                :    0.54
 
 Sample variance                       :    1.17
 p-value of test no 254                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:57.13
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35986
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 3                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:01.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 4                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1361
 p-value of test no 5                  :    0.53
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334481
   j =  1                              :        599997278
   j =  2                              :             1361
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:48.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 6                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 7                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:49.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 8                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:10.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 9                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 10                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:07.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1510
 p-value of test no 11                 :  5.4e-5    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334630
   j =  1                              :        599996980
   j =  2                              :             1510
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 12                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5444
 p-value of test no 13                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4258
 p-value of test no 14                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7369
 p-value of test no 15                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4242
 p-value of test no 17                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7136
 p-value of test no 19                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7345
 p-value of test no 20                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7449
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.38
 p-value of test no 22                 :    0.21
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.86
 p-value of test no 23                 :    0.44
 
 Test on the Nm values of W_{n,i}(mNP1):    0.67
 p-value of test no 24                 :    0.59
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     915
 p-value of test no 25                 :    0.31
 
 Stat. AD (mNP2)                       :    0.17
 p-value of test no 26                 :    0.9963
 
 Stat. AD after spacings (mNP2-S)      :    0.60
 p-value of test no 27                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.87
 p-value of test no 28                 :    0.43
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.83
 p-value of test no 29                 :    0.46
 
 Test on the Nm values of W_{n,i}(mNP1):    2.39
 p-value of test no 30                 :    0.06
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     655
 p-value of test no 31                 :    0.01
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 32                 :    0.77
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 33                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.63
 p-value of test no 34                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.62
 p-value of test no 35                 :    0.62
 
 Test on the Nm values of W_{n,i}(mNP1):    3.08
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     262
 p-value of test no 37                 :    0.99
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 38                 :    0.54
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 39                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 40                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 41                 :    0.69
 
 Test on the Nm values of W_{n,i}(mNP1):    0.47
 p-value of test no 42                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     159
 p-value of test no 43                 :    0.24
 
 Stat. AD (mNP2)                       :    0.29
 p-value of test no 44                 :    0.94
 
 Stat. AD after spacings (mNP2-S)      :    0.72
 p-value of test no 45                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.10
 p-value of test no 46                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.15
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.34
 p-value of test no 48                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.26
 p-value of test no 49                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.05
 p-value of test no 50                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   43.66
 p-value of test no 51                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.19
 p-value of test no 52                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   38.80
 p-value of test no 53                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  219.47
 p-value of test no 54                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  403.71
 p-value of test no 55                 :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1352.98
 p-value of test no 56                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6861.79
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 58                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 59                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 60                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   31.69
 p-value of test no 61                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 62                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 64                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   61.71
 p-value of test no 65                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.73
 p-value of test no 66                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  127.03
 p-value of test no 67                 :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5092.07
 p-value of test no 68                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:56.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45998
 p-value of test no 70                 :    0.29
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869998
   j =  1                              :        399908007
   j =  2                              :            45992
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46572
 p-value of test no 71                 :  6.3e-4    *****
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870572
   j =  1                              :        399906858
   j =  2                              :            46568
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:38.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.069
 p-value of test no 72                 :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 73                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 74                 :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.43
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 77                 :    0.37
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 78                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.024
 p-value of test no 79                 :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.09
 
 Anderson-Darling statistic = A2       :    1.58
 p-value of test no 81                 :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.07
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 83                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 84                 :    0.62
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 85                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:47.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 86                 :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 87                 :    0.29
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 88                 :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.25
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 90                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 91                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 92                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.086
 p-value of test no 93                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 95                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
 p-value of test no 97                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 98                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.94
 p-value of test no 99                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.048
 p-value of test no 101                :    0.81
 
 Anderson-Darling statistic = A2       :    2.32
 p-value of test no 102                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 103                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 104                :    0.41
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 105                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 106                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.16
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 108                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 109                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
 p-value of test no 110                :    0.71
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 111                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
 p-value of test no 112                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
 p-value of test no 113                :    0.10
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 114                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.30
 p-value of test no 115                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.64
 p-value of test no 116                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.33
 p-value of test no 117                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.041
 p-value of test no 118                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.21
 p-value of test no 119                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   49.04
 p-value of test no 120                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.94
 p-value of test no 121                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.73
 p-value of test no 122                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.53
 p-value of test no 123                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.87
 p-value of test no 124                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   19.00
 p-value of test no 125                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 126                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 127                :    0.62
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 128                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.91
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.026
 p-value of test no 130                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.42
 p-value of test no 131                :    0.02
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 132                :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   56.07
 p-value of test no 133                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.03
 p-value of test no 134                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.02
 p-value of test no 135                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.81
 p-value of test no 137                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.63
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 140                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  116.07
 p-value of test no 141                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 142                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 143                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 144                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17471.26
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   22.18
 p-value of test no 146                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.27
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.92
 p-value of test no 148                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.12
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.31
 p-value of test no 150                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.08
 p-value of test no 151                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   32.22
 p-value of test no 152                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.45
 p-value of test no 153                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   26.17
 p-value of test no 154                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.78
 p-value of test no 155                :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  148.49
 p-value of test no 156                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.01
 p-value of test no 157                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  469.11
 p-value of test no 158                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.84
 p-value of test no 159                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.30
 p-value of test no 160                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.18
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  123.23
 p-value of test no 162                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  496.20
 p-value of test no 163                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.43
 p-value of test no 164                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   67.53
 p-value of test no 165                :    0.69
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  355.42
 p-value of test no 166                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.96
 p-value of test no 167                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4974.80
 p-value of test no 168                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.48
 p-value of test no 169                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  191.61
 p-value of test no 170                :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.27
 p-value of test no 171                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  387.52
 p-value of test no 172                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4911.55
 p-value of test no 173                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  359.13
 p-value of test no 174                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  192.03
 p-value of test no 175                :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.44
 p-value of test no 176                :    0.49
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.48
 p-value of test no 177                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.91
 p-value of test no 178                :    0.20
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.66
 p-value of test no 179                :    0.26
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.065
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.06
 
 Anderson-Darling statistic = A2       :    1.73
 p-value of test no 182                :    0.13
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.43
 p-value of test no 183                :    0.08
 
 Sample variance                       :    0.35
 p-value of test no 184                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 185                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 186                :    0.60
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 187                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.23
 p-value of test no 188                :    0.41
 
 Sample variance                       :    0.60
 p-value of test no 189                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
 p-value of test no 190                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
 p-value of test no 191                :    0.75
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 192                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
 p-value of test no 194                :    0.92
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 195                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.96
 p-value of test no 196                :    0.54
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.39
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.080
 p-value of test no 200                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.66
 p-value of test no 202                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.88
 p-value of test no 203                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.26
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  204.21
 p-value of test no 207                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 208                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 209                :    0.55
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 210                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10005.67
 p-value of test no 211                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 212                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 213                :    0.21
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 214                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10094.43
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.042
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.095
 p-value of test no 217                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.27
 p-value of test no 218                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 219                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
 p-value of test no 220                :    0.9949
 
 Anderson-Darling statistic = A2       :    2.89
 p-value of test no 221                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4659.34
 p-value of test no 222                :    0.9909
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.057
 p-value of test no 224                :    0.91
 
 Anderson-Darling statistic = A2       :    2.11
 p-value of test no 225                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4707.35
 p-value of test no 226                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3931.28
 p-value of test no 227                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4159.29
 p-value of test no 228                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12141.13
 p-value of test no 229                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12006.12
 p-value of test no 230                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   50.32
 p-value of test no 231                :    0.62
 
 
 -----------------------------------------------
 Total number of bits:  8000043960
 
 Normal statistic for number of bits   :    0.35
 p-value of test no 232                :    0.36
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   46.95
 p-value of test no 233                :    0.74
 
 
 -----------------------------------------------
 Total number of bits:  8000089734
 
 Normal statistic for number of bits   :    0.71
 p-value of test no 234                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 235                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 236                :    0.66
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.14
 p-value of test no 238                :    0.44
 
 Sample variance                       :    0.66
 p-value of test no 239                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.43
 p-value of test no 240                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :   0.054
 p-value of test no 241                :    0.91
 
 Anderson-Darling statistic = A2       :    2.26
 p-value of test no 242                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.64
 p-value of test no 243                :    0.95
 
 Sample variance                       :    0.32
 p-value of test no 244                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.57
 p-value of test no 248                :    0.28
 
 Sample variance                       :    0.81
 p-value of test no 249                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 251                :    0.69
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 252                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.93
 p-value of test no 253                :    0.82
 
 Sample variance                       :    1.67
 p-value of test no 254                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:34.84
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           5.4e-5
  45  CollisionPermut, r = 10         6.3e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35987
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 3                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1328
 p-value of test no 4                  :    0.83
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334448
   j =  1                              :        599997344
   j =  2                              :             1328
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1321
 p-value of test no 5                  :    0.88
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334441
   j =  1                              :        599997358
   j =  2                              :             1321
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.49
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 8                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:08.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 9                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1401
 p-value of test no 10                 :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334521
   j =  1                              :        599997198
   j =  2                              :             1401
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1309
 p-value of test no 11                 :    0.93
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334429
   j =  1                              :        599997382
   j =  2                              :             1309
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 12                 :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5378
 p-value of test no 13                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4434
 p-value of test no 14                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7437
 p-value of test no 15                 :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 16                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 17                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 18                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7218
 p-value of test no 19                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7271
 p-value of test no 20                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7162
 p-value of test no 21                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.38
 p-value of test no 22                 :    0.86
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.46
 p-value of test no 23                 :    0.79
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     875
 p-value of test no 25                 :    0.79
 
 Stat. AD (mNP2)                       :    0.66
 p-value of test no 26                 :    0.59
 
 Stat. AD after spacings (mNP2-S)      :    1.58
 p-value of test no 27                 :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 28                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 29                 :    0.75
 
 Test on the Nm values of W_{n,i}(mNP1):    0.77
 p-value of test no 30                 :    0.50
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    0.87
 p-value of test no 32                 :    0.43
 
 Stat. AD after spacings (mNP2-S)      :    1.77
 p-value of test no 33                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.93
 p-value of test no 34                 :    0.39
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.81
 p-value of test no 35                 :    0.47
 
 Test on the Nm values of W_{n,i}(mNP1):    0.45
 p-value of test no 36                 :    0.80
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     307
 p-value of test no 37                 :    0.35
 
 Stat. AD (mNP2)                       :    0.82
 p-value of test no 38                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.25
 p-value of test no 39                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.45
 p-value of test no 40                 :    0.79
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.40
 p-value of test no 41                 :    0.84
 
 Test on the Nm values of W_{n,i}(mNP1):    1.57
 p-value of test no 42                 :    0.16
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     162
 p-value of test no 43                 :    0.17
 
 Stat. AD (mNP2)                       :    1.43
 p-value of test no 44                 :    0.19
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.68
 p-value of test no 46                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.03
 p-value of test no 47                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.54
 p-value of test no 48                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.68
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.49
 p-value of test no 50                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.43
 p-value of test no 51                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.98
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.96
 p-value of test no 53                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  257.55
 p-value of test no 54                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  462.53
 p-value of test no 55                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1358.47
 p-value of test no 56                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6975.07
 p-value of test no 57                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 58                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 60                 :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.27
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 62                 :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 63                 :    0.88
 
 Anderson-Darling statistic = A2       :    1.83
 p-value of test no 64                 :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   41.46
 p-value of test no 65                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   18.18
 p-value of test no 66                 :  2.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.11
 p-value of test no 67                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5116.04
 p-value of test no 68                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46249
 p-value of test no 70                 :    0.04
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870249
   j =  1                              :        399907506
   j =  2                              :            46241
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46060
 p-value of test no 71                 :    0.20
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870060
   j =  1                              :        399907883
   j =  2                              :            46054
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
 p-value of test no 73                 :    0.99
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 74                 :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.90
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 77                 :    0.71
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 79                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 80                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 81                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.34
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 83                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 84                 :    0.26
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 85                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.085
 p-value of test no 86                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 88                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 90                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    1.59
 p-value of test no 92                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 93                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 94                 :    0.69
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 95                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.73
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.46
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 99                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 100                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.018
 p-value of test no 101                :    0.96
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 102                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 103                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 105                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 106                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 107                :    0.06
 
 Anderson-Darling statistic = A2       :    1.82
 p-value of test no 108                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.10e-4
 p-value of test no 109                :  1.2e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
 p-value of test no 110                :    0.92
 
 Anderson-Darling statistic = A2       :    4.28
 p-value of test no 111                :  6.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.68e-5
 p-value of test no 112                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
 p-value of test no 113                :    0.06
 
 Anderson-Darling statistic = A2       :    2.68
 p-value of test no 114                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 115                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.51
 p-value of test no 116                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.21
 p-value of test no 117                :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.15
 p-value of test no 118                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.62
 p-value of test no 119                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   56.89
 p-value of test no 120                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.18
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.49
 p-value of test no 122                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   40.48
 p-value of test no 123                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   42.15
 p-value of test no 124                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.84
 p-value of test no 125                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.38
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 128                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.70
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 130                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 131                :    0.51
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 132                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.65
 p-value of test no 133                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.74
 p-value of test no 134                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.92
 p-value of test no 135                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    4.07
 p-value of test no 136                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.60
 p-value of test no 137                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 138                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 140                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.25
 p-value of test no 141                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 143                :    0.06
 
 Anderson-Darling statistic = A2       :    1.10
 p-value of test no 144                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17617.53
 p-value of test no 145                :    0.16
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.87
 p-value of test no 146                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   25.00
 p-value of test no 147                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.83
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   19.16
 p-value of test no 149                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.66
 p-value of test no 150                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.78
 p-value of test no 151                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.14
 p-value of test no 152                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.25
 p-value of test no 153                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   18.20
 p-value of test no 154                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   39.18
 p-value of test no 155                :  1.7e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :   85.16
 p-value of test no 156                : 1 -  1.4e-5    *****
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.04
 p-value of test no 157                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  540.74
 p-value of test no 158                :    0.10
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  151.28
 p-value of test no 159                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   65.10
 p-value of test no 160                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.47
 p-value of test no 161                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  150.19
 p-value of test no 162                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.92
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  131.31
 p-value of test no 164                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.28
 p-value of test no 165                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.83
 p-value of test no 166                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  363.90
 p-value of test no 167                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5099.04
 p-value of test no 168                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  451.35
 p-value of test no 169                :  5.6e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  186.94
 p-value of test no 170                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.65
 p-value of test no 171                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.55
 p-value of test no 172                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4970.48
 p-value of test no 173                :    0.61
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  372.26
 p-value of test no 174                :    0.57
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  175.11
 p-value of test no 175                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.93
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.71
 p-value of test no 177                :    0.24
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   16.56
 p-value of test no 178                :    0.17
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.43
 p-value of test no 179                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 181                :    0.76
 
 Anderson-Darling statistic = A2       :    0.99
 p-value of test no 182                :    0.36
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.92
 p-value of test no 183                :    0.82
 
 Sample variance                       :    0.53
 p-value of test no 184                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 185                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 186                :    0.73
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 187                :    0.89
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 188                :    0.64
 
 Sample variance                       :    0.62
 p-value of test no 189                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
 p-value of test no 190                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 191                :    0.32
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 192                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 193                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
 p-value of test no 194                :    0.57
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 195                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   19.74
 p-value of test no 196                :    0.01
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.41
 p-value of test no 198                :    0.71
 
 -----------------------------------------------
 Global longest run of 1               :   37.00
 p-value of test no 199                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 200                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 201                :    0.25
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 202                :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  218.12
 p-value of test no 203                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 204                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 205                :    0.75
 
 Anderson-Darling statistic = A2       :    1.25
 p-value of test no 206                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.37
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 208                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 209                :    0.62
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 210                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9937.66
 p-value of test no 211                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 212                :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 213                :    0.55
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 214                :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9993.38
 p-value of test no 215                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.61
 p-value of test no 216                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.57
 p-value of test no 217                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 219                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 220                :    0.03
 
 Anderson-Darling statistic = A2       :    2.29
 p-value of test no 221                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5074.41
 p-value of test no 222                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 223                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 224                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 225                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4890.57
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4053.54
 p-value of test no 227                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4138.78
 p-value of test no 228                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11849.08
 p-value of test no 229                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11668.48
 p-value of test no 230                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   71.05
 p-value of test no 231                :    0.06
 
 
 -----------------------------------------------
 Total number of bits:  8000054529
 
 Normal statistic for number of bits   :    0.43
 p-value of test no 232                :    0.33
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   47.84
 p-value of test no 233                :    0.71
 
 
 -----------------------------------------------
 Total number of bits:  8000039301
 
 Normal statistic for number of bits   :    0.31
 p-value of test no 234                :    0.38
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 235                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.50
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 237                :    0.68
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.52
 p-value of test no 238                :    0.70
 
 Sample variance                       :    1.61
 p-value of test no 239                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 240                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 241                :    0.84
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 242                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.01
 p-value of test no 243                :    0.84
 
 Sample variance                       :    1.95
 p-value of test no 244                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 245                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 247                :    0.58
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.74
 p-value of test no 248                :    0.77
 
 Sample variance                       :    0.52
 p-value of test no 249                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.42
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 252                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.17
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.57
 p-value of test no 254                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.64
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:48.86
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  76  RandomWalk1 H (L=1000, r=0)    1 -  1.4e-5
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35988
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.77
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 3                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 4                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 5                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1372
 p-value of test no 6                  :    0.42
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334492
   j =  1                              :        599997256
   j =  2                              :             1372
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:09.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 7                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:46.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 9                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.99
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 10                 :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 11                 :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1281
 p-value of test no 12                 :    0.99
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334401
   j =  1                              :        599997438
   j =  2                              :             1281
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5342
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4378
 p-value of test no 14                 :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7435
 p-value of test no 15                 :    0.09
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4360
 p-value of test no 16                 :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4272
 p-value of test no 17                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7229
 p-value of test no 18                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7267
 p-value of test no 19                 :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7258
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7119
 p-value of test no 21                 :    0.9902
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 22                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.90
 p-value of test no 23                 :    0.41
 
 Test on the Nm values of W_{n,i}(mNP1):    0.94
 p-value of test no 24                 :    0.39
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     931
 p-value of test no 25                 :    0.15
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    0.67
 p-value of test no 27                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.75
 p-value of test no 28                 :    0.13
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.88
 p-value of test no 29                 :    0.42
 
 Test on the Nm values of W_{n,i}(mNP1):    0.29
 p-value of test no 30                 :    0.95
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    1.14
 p-value of test no 32                 :    0.29
 
 Stat. AD after spacings (mNP2-S)      :    0.62
 p-value of test no 33                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.64
 p-value of test no 34                 :    0.61
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 35                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.21
 p-value of test no 36                 :    0.99
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     290
 p-value of test no 37                 :    0.71
 
 Stat. AD (mNP2)                       :    0.62
 p-value of test no 38                 :    0.63
 
 Stat. AD after spacings (mNP2-S)      :    0.34
 p-value of test no 39                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.19
 p-value of test no 40                 :    0.27
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.50
 p-value of test no 41                 :    0.74
 
 Test on the Nm values of W_{n,i}(mNP1):    0.86
 p-value of test no 42                 :    0.44
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     145
 p-value of test no 43                 :    0.64
 
 Stat. AD (mNP2)                       :    0.69
 p-value of test no 44                 :    0.57
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.91
 p-value of test no 46                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.55
 p-value of test no 47                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.80
 p-value of test no 48                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.73
 p-value of test no 49                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.71
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.97
 p-value of test no 51                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   59.66
 p-value of test no 52                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   50.45
 p-value of test no 53                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  215.88
 p-value of test no 54                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  405.14
 p-value of test no 55                 :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1419.09
 p-value of test no 56                 :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7377.33
 p-value of test no 57                 :  2.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 58                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 59                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.58
 p-value of test no 61                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 62                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 64                 :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.26
 p-value of test no 65                 :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   10.48
 p-value of test no 66                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  124.59
 p-value of test no 67                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5120.92
 p-value of test no 68                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45657
 p-value of test no 70                 :    0.85
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869657
   j =  1                              :        399908690
   j =  2                              :            45649
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45810
 p-value of test no 71                 :    0.63
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869810
   j =  1                              :        399908382
   j =  2                              :            45806
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 72                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.37
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 74                 :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 77                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.57
 p-value of test no 78                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.057
 p-value of test no 79                 :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 80                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 81                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.15
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 83                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 84                 :    0.21
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 85                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 87                 :    0.20
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 88                 :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 90                 :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 91                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 92                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 93                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 94                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 95                 :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.47
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 97                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 98                 :    0.36
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 99                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.043
 p-value of test no 100                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 101                :    0.01
 
 Anderson-Darling statistic = A2       :    4.03
 p-value of test no 102                :  8.5e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 103                :  9.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.019
 p-value of test no 104                :    0.97
 
 Anderson-Darling statistic = A2       :    4.32
 p-value of test no 105                :  6.3e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.28
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 108                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
 p-value of test no 109                :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
 p-value of test no 110                :    0.09
 
 Anderson-Darling statistic = A2       :    1.86
 p-value of test no 111                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
 p-value of test no 112                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
 p-value of test no 113                :    0.80
 
 Anderson-Darling statistic = A2       :    1.50
 p-value of test no 114                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    1.73
 p-value of test no 116                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.02
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.41
 p-value of test no 118                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.67
 p-value of test no 119                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.28
 p-value of test no 120                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   82.31
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.88
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.16
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.40
 p-value of test no 124                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   23.64
 p-value of test no 125                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 126                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 127                :    0.53
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 128                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   37.97
 p-value of test no 129                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.24
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   42.15
 p-value of test no 133                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.04
 p-value of test no 134                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.34
 p-value of test no 135                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   12.54
 p-value of test no 136                :  1.9e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 138                :  8.5e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.084
 p-value of test no 139                :    0.83
 
 Anderson-Darling statistic = A2       :    3.00
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :   98.03
 p-value of test no 141                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.40
 p-value of test no 142                :    0.03
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 143                :    0.88
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 144                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17175.75
 p-value of test no 145                :    0.91
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   21.18
 p-value of test no 146                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.18
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   40.26
 p-value of test no 148                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.84
 p-value of test no 149                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.54
 p-value of test no 150                :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   41.55
 p-value of test no 151                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.42
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.34
 p-value of test no 153                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.25
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   16.78
 p-value of test no 155                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.29
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  173.00
 p-value of test no 157                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  509.61
 p-value of test no 158                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  135.37
 p-value of test no 159                :    0.50
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   88.33
 p-value of test no 160                :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  153.09
 p-value of test no 161                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  144.00
 p-value of test no 162                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  463.89
 p-value of test no 163                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  104.37
 p-value of test no 164                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.82
 p-value of test no 165                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.11
 p-value of test no 166                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.44
 p-value of test no 167                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5020.06
 p-value of test no 168                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  376.05
 p-value of test no 169                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  188.65
 p-value of test no 170                :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.00
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  364.50
 p-value of test no 172                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4836.92
 p-value of test no 173                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  326.76
 p-value of test no 174                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.63
 p-value of test no 175                :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.94
 p-value of test no 176                :    0.79
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.41
 p-value of test no 177                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   29.22
 p-value of test no 178                :  3.7e-3
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.59
 p-value of test no 179                :    0.72
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 180                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 181                :    0.37
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 182                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.67
 p-value of test no 183                :    0.25
 
 Sample variance                       :    0.59
 p-value of test no 184                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 186                :    0.47
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.55
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.43
 p-value of test no 188                :    0.33
 
 Sample variance                       :    1.93
 p-value of test no 189                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
 p-value of test no 190                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 192                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
 p-value of test no 193                :    0.82
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.29
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 195                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.37
 p-value of test no 196                :    0.91
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    2.40
 p-value of test no 198                :    0.97
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 200                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.65
 
 Anderson-Darling statistic = A2       :    1.08
 p-value of test no 202                :    0.31
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  178.50
 p-value of test no 203                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.071
 p-value of test no 204                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.36
 p-value of test no 206                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  235.28
 p-value of test no 207                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 208                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 209                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 210                :    0.65
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9882.08
 p-value of test no 211                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
 p-value of test no 212                :    0.9910
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 213                :    0.03
 
 Anderson-Darling statistic = A2       :    2.56
 p-value of test no 214                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10316.22
 p-value of test no 215                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.16
 p-value of test no 216                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.48
 p-value of test no 217                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.68
 p-value of test no 218                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 219                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 220                :    0.92
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4834.48
 p-value of test no 222                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 223                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 224                :    0.03
 
 Anderson-Darling statistic = A2       :    2.07
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5050.83
 p-value of test no 226                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4131.82
 p-value of test no 227                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4102.82
 p-value of test no 228                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12049.34
 p-value of test no 229                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12095.72
 p-value of test no 230                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.24
 p-value of test no 231                :    0.58
 
 
 -----------------------------------------------
 Total number of bits:  8000168970
 
 Normal statistic for number of bits   :    1.34
 p-value of test no 232                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   65.49
 p-value of test no 233                :    0.14
 
 
 -----------------------------------------------
 Total number of bits:  7999989555
 
 Normal statistic for number of bits   :  -0.083
 p-value of test no 234                :    0.53
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.066
 p-value of test no 235                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 237                :    0.96
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 238                :    0.35
 
 Sample variance                       :    0.86
 p-value of test no 239                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 240                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 241                :    0.27
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 242                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.31
 p-value of test no 243                :    0.09
 
 Sample variance                       :    1.42
 p-value of test no 244                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 246                :    0.30
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 247                :    0.45
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.35
 p-value of test no 248                :    0.37
 
 Sample variance                       :    1.48
 p-value of test no 249                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 250                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.56
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.48
 p-value of test no 253                :    0.68
 
 Sample variance                       :    1.30
 p-value of test no 254                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.68
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:44.20
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35989
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.64
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 3                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1323
 p-value of test no 4                  :    0.87
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334443
   j =  1                              :        599997354
   j =  2                              :             1323
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1346
 p-value of test no 5                  :    0.68
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334466
   j =  1                              :        599997308
   j =  2                              :             1346
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:45.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1387
 p-value of test no 6                  :    0.27
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334507
   j =  1                              :        599997226
   j =  2                              :             1387
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 7                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1336
 p-value of test no 8                  :    0.77
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334456
   j =  1                              :        599997328
   j =  2                              :             1336
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.74
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1381
 p-value of test no 9                  :    0.33
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334501
   j =  1                              :        599997238
   j =  2                              :             1381
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1314
 p-value of test no 10                 :    0.91
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334434
   j =  1                              :        599997372
   j =  2                              :             1314
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1269
 p-value of test no 11                 :    0.9952
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334389
   j =  1                              :        599997462
   j =  2                              :             1269
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1439
 p-value of test no 12                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334559
   j =  1                              :        599997122
   j =  2                              :             1439
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5440
 p-value of test no 13                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4333
 p-value of test no 14                 :    0.52
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7355
 p-value of test no 15                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4384
 p-value of test no 16                 :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4255
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7291
 p-value of test no 18                 :    0.62
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7189
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7285
 p-value of test no 20                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7263
 p-value of test no 21                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 22                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.30
 p-value of test no 23                 :    0.23
 
 Test on the Nm values of W_{n,i}(mNP1):    0.38
 p-value of test no 24                 :    0.86
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     928
 p-value of test no 25                 :    0.18
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 26                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    2.50
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.32
 p-value of test no 28                 :    0.92
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.23
 p-value of test no 29                 :    0.98
 
 Test on the Nm values of W_{n,i}(mNP1):    0.56
 p-value of test no 30                 :    0.69
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     603
 p-value of test no 31                 :    0.46
 
 Stat. AD (mNP2)                       :    0.58
 p-value of test no 32                 :    0.67
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.56
 p-value of test no 34                 :    0.68
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.93
 p-value of test no 35                 :    0.40
 
 Test on the Nm values of W_{n,i}(mNP1):    0.54
 p-value of test no 36                 :    0.71
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.47
 p-value of test no 38                 :    0.78
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 39                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.52
 p-value of test no 40                 :    0.72
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.25
 p-value of test no 41                 :    0.97
 
 Test on the Nm values of W_{n,i}(mNP1):    1.84
 p-value of test no 42                 :    0.11
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     140
 p-value of test no 43                 :    0.78
 
 Stat. AD (mNP2)                       :    0.34
 p-value of test no 44                 :    0.90
 
 Stat. AD after spacings (mNP2-S)      :    2.32
 p-value of test no 45                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.83
 p-value of test no 46                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.61
 p-value of test no 47                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.80
 p-value of test no 48                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    8.22
 p-value of test no 49                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.16
 p-value of test no 50                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   69.92
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.87
 p-value of test no 52                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 53                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  235.14
 p-value of test no 54                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  449.05
 p-value of test no 55                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.40
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7157.64
 p-value of test no 57                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 58                 :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.30
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 60                 :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   37.35
 p-value of test no 61                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 62                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.095
 p-value of test no 63                 :    0.79
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 64                 :    0.64
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   60.02
 p-value of test no 65                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  128.88
 p-value of test no 67                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5156.00
 p-value of test no 68                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45783
 p-value of test no 70                 :    0.67
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869783
   j =  1                              :        399908434
   j =  2                              :            45783
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45672
 p-value of test no 71                 :    0.83
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869672
   j =  1                              :        399908658
   j =  2                              :            45668
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
 p-value of test no 72                 :    0.9931
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 73                 :  3.4e-3
 
 Anderson-Darling statistic = A2       :    3.65
 p-value of test no 74                 :    0.01
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :  4.1e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.043
 p-value of test no 77                 :    0.84
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 78                 :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.030
 p-value of test no 79                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 80                 :    0.27
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.14
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 84                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 85                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 86                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 87                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 88                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 90                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 91                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 92                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 93                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 94                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.92
 p-value of test no 95                 :    0.40
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 97                 :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 98                 :    0.23
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 99                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 100                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 101                :    0.44
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 102                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 104                :    0.87
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 106                :    0.13
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 107                :    0.79
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 108                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
 p-value of test no 109                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
 p-value of test no 110                :    0.54
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 111                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
 p-value of test no 112                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
 p-value of test no 113                :    0.63
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 114                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 115                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 117                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.73
 p-value of test no 118                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.26
 p-value of test no 119                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.57
 p-value of test no 120                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.47
 p-value of test no 121                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.42
 p-value of test no 122                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.49
 p-value of test no 123                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.74
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   42.62
 p-value of test no 125                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.070
 p-value of test no 126                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.43
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 128                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.08
 p-value of test no 129                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 130                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.096
 p-value of test no 131                :    0.78
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 132                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   36.48
 p-value of test no 133                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.77
 p-value of test no 134                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    4.87
 p-value of test no 135                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.19
 p-value of test no 136                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:12.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.44
 p-value of test no 137                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 138                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 139                :    0.41
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 140                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  140.56
 p-value of test no 141                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.089
 p-value of test no 142                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 143                :    0.24
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 144                :    0.43
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17627.89
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.56
 p-value of test no 146                :    0.84
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   33.90
 p-value of test no 147                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   32.08
 p-value of test no 148                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.63
 p-value of test no 149                :    0.54
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   32.88
 p-value of test no 150                :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.61
 p-value of test no 151                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.56
 p-value of test no 152                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.60
 p-value of test no 153                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   23.02
 p-value of test no 154                :    0.52
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.39
 p-value of test no 155                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  137.14
 p-value of test no 156                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  133.97
 p-value of test no 157                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.63
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  134.23
 p-value of test no 159                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   62.27
 p-value of test no 160                :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.21
 p-value of test no 161                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.05
 p-value of test no 162                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  481.88
 p-value of test no 163                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  133.27
 p-value of test no 164                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   75.38
 p-value of test no 165                :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  358.25
 p-value of test no 166                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  390.11
 p-value of test no 167                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5089.24
 p-value of test no 168                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.60
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  214.09
 p-value of test no 170                :    0.24
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  417.55
 p-value of test no 171                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  353.11
 p-value of test no 172                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5113.54
 p-value of test no 173                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  418.88
 p-value of test no 174                :    0.07
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  229.88
 p-value of test no 175                :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.84
 p-value of test no 176                :    0.72
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.09
 p-value of test no 177                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   22.15
 p-value of test no 178                :    0.04
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.22
 p-value of test no 179                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 180                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 181                :    0.83
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 182                :    0.51
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.88
 p-value of test no 183                :    0.81
 
 Sample variance                       :    0.66
 p-value of test no 184                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 185                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 187                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.054
 p-value of test no 188                :    0.52
 
 Sample variance                       :    0.66
 p-value of test no 189                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
 p-value of test no 190                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.23
 p-value of test no 192                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 193                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
 p-value of test no 194                :    0.84
 
 Anderson-Darling statistic = A2       :    1.61
 p-value of test no 195                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.97
 p-value of test no 196                :    0.15
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.54
 p-value of test no 198                :    0.30
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.63
 p-value of test no 200                :  9.9e-5    *****
 
 Kolmogorov-Smirnov- statistic = D-    :   0.021
 p-value of test no 201                :    0.97
 
 Anderson-Darling statistic = A2       :    6.56
 p-value of test no 202                :  5.8e-4    *****
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  140.11
 p-value of test no 203                :    0.9996    *****
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 204                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 205                :    0.23
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 206                :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  219.35
 p-value of test no 207                :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 208                :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 209                :    0.60
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 210                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9963.29
 p-value of test no 211                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.050
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.24
 p-value of test no 214                :    0.25
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9806.73
 p-value of test no 215                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.055
 p-value of test no 216                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.89
 p-value of test no 217                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.24
 p-value of test no 218                :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :   0.089
 p-value of test no 220                :    0.81
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 221                :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4843.04
 p-value of test no 222                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 223                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 224                :    0.60
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 225                :    0.33
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4857.01
 p-value of test no 226                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4285.26
 p-value of test no 227                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4265.64
 p-value of test no 228                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11929.63
 p-value of test no 229                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11944.41
 p-value of test no 230                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   63.30
 p-value of test no 231                :    0.18
 
 
 -----------------------------------------------
 Total number of bits:  8000231583
 
 Normal statistic for number of bits   :    1.83
 p-value of test no 232                :    0.03
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   62.20
 p-value of test no 233                :    0.21
 
 
 -----------------------------------------------
 Total number of bits:  8000031441
 
 Normal statistic for number of bits   :    0.25
 p-value of test no 234                :    0.40
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 235                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 236                :    0.56
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 237                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.36
 p-value of test no 238                :    0.64
 
 Sample variance                       :    1.66
 p-value of test no 239                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 240                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 241                :    0.69
 
 Anderson-Darling statistic = A2       :    0.20
 p-value of test no 242                :    0.99
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.085
 p-value of test no 243                :    0.47
 
 Sample variance                       :    1.05
 p-value of test no 244                :    0.40
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 245                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.46
 
 Anderson-Darling statistic = A2       :    0.28
 p-value of test no 247                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.060
 p-value of test no 248                :    0.48
 
 Sample variance                       :    0.65
 p-value of test no 249                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 250                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 252                :    0.57
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.11
 p-value of test no 253                :    0.13
 
 Sample variance                       :    1.37
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.44
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  88  PeriodsInStrings, r = 0         0.9996 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35990
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 3                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 4                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:21.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 5                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:47.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 6                  :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 7                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 8                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 9                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 10                 :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1481
 p-value of test no 12                 :  9.4e-4    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334601
   j =  1                              :        599997038
   j =  2                              :             1481
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5363
 p-value of test no 13                 :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4306
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7238
 p-value of test no 15                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4338
 p-value of test no 16                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4324
 p-value of test no 17                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7362
 p-value of test no 18                 :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7240
 p-value of test no 19                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7338
 p-value of test no 20                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7302
 p-value of test no 21                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:09.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.67
 p-value of test no 22                 :    0.58
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 24                 :    0.78
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     893
 p-value of test no 25                 :    0.58
 
 Stat. AD (mNP2)                       :    0.49
 p-value of test no 26                 :    0.75
 
 Stat. AD after spacings (mNP2-S)      :    1.34
 p-value of test no 27                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.68
 p-value of test no 28                 :    0.57
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.55
 p-value of test no 29                 :    0.70
 
 Test on the Nm values of W_{n,i}(mNP1):    0.98
 p-value of test no 30                 :    0.37
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.13
 p-value of test no 33                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.21
 p-value of test no 34                 :    0.99
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.98
 p-value of test no 35                 :    0.36
 
 Test on the Nm values of W_{n,i}(mNP1):    3.32
 p-value of test no 36                 :    0.02
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     358
 p-value of test no 37                 :  6.2e-4    *****
 
 Stat. AD (mNP2)                       :    0.46
 p-value of test no 38                 :    0.79
 
 Stat. AD after spacings (mNP2-S)      :    1.12
 p-value of test no 39                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:02:03.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.83
 p-value of test no 40                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.30
 p-value of test no 41                 :    0.94
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 42                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     160
 p-value of test no 43                 :    0.22
 
 Stat. AD (mNP2)                       :    2.28
 p-value of test no 44                 :    0.06
 
 Stat. AD after spacings (mNP2-S)      :    0.32
 p-value of test no 45                 :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   15.67
 p-value of test no 46                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    3.65
 p-value of test no 47                 :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   21.39
 p-value of test no 48                 :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.35
 p-value of test no 49                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.29
 p-value of test no 50                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.98
 p-value of test no 51                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.00
 p-value of test no 52                 :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   65.83
 p-value of test no 53                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  218.17
 p-value of test no 54                 :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  431.55
 p-value of test no 55                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1506.05
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7096.64
 p-value of test no 57                 :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 58                 :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 59                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 60                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.37
 p-value of test no 61                 :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 62                 :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 63                 :    0.39
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 64                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   64.02
 p-value of test no 65                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.81
 p-value of test no 66                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.29
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5043.00
 p-value of test no 68                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.79
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45538
 p-value of test no 70                 :    0.94
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869538
   j =  1                              :        399908926
   j =  2                              :            45534
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45975
 p-value of test no 71                 :    0.33
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869975
   j =  1                              :        399908053
   j =  2                              :            45969
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 72                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 73                 :    0.34
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 74                 :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.30
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.098
 p-value of test no 76                 :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :   0.014
 p-value of test no 77                 :    0.98
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 78                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 81                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.31
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 83                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 84                 :    0.94
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 85                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:44.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 86                 :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 87                 :    0.07
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 88                 :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.09
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 90                 :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 91                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 92                 :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 93                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.33
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 95                 :    0.70
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.39
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 97                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 98                 :    0.12
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 99                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 100                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :   0.075
 p-value of test no 101                :    0.60
 
 Anderson-Darling statistic = A2       :    1.18
 p-value of test no 102                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 103                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 104                :    0.53
 
 Anderson-Darling statistic = A2       :    1.38
 p-value of test no 105                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 106                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 107                :    0.59
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 108                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.28e-5
 p-value of test no 109                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
 p-value of test no 110                :    0.05
 
 Anderson-Darling statistic = A2       :    1.68
 p-value of test no 111                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
 p-value of test no 112                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    : 8.63e-5
 p-value of test no 113                :    0.74
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 114                :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.55
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.41
 p-value of test no 116                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.32
 p-value of test no 118                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   72.13
 p-value of test no 119                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   51.64
 p-value of test no 120                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   53.08
 p-value of test no 121                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.86
 p-value of test no 122                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.26
 p-value of test no 123                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.12
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   41.51
 p-value of test no 125                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.032
 p-value of test no 126                :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 127                :    0.42
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 128                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.99
 p-value of test no 129                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 130                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 132                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   25.08
 p-value of test no 133                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.13
 p-value of test no 134                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    7.26
 p-value of test no 135                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.49
 p-value of test no 136                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 137                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 138                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 139                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 140                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  131.80
 p-value of test no 141                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 142                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.041
 p-value of test no 143                :    0.94
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 144                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17300.94
 p-value of test no 145                :    0.75
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.13
 p-value of test no 146                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   41.64
 p-value of test no 147                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.67
 p-value of test no 148                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.01
 p-value of test no 149                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   23.53
 p-value of test no 150                :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   35.45
 p-value of test no 151                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.69
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   30.79
 p-value of test no 153                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.39
 p-value of test no 154                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.05
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  154.80
 p-value of test no 156                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.87
 p-value of test no 157                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  508.42
 p-value of test no 158                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  127.76
 p-value of test no 159                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   78.06
 p-value of test no 160                :    0.35
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.56
 p-value of test no 161                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  140.15
 p-value of test no 162                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  520.94
 p-value of test no 163                :    0.25
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  124.28
 p-value of test no 164                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   68.03
 p-value of test no 165                :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  366.83
 p-value of test no 166                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  428.43
 p-value of test no 167                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4962.67
 p-value of test no 168                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  370.55
 p-value of test no 169                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  199.55
 p-value of test no 170                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.96
 p-value of test no 171                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.30
 p-value of test no 172                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4985.73
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  344.49
 p-value of test no 174                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  241.72
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    8.59
 p-value of test no 176                :    0.74
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  : -5.96e-3
 p-value of test no 177                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    6.76
 p-value of test no 178                :    0.87
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.64
 p-value of test no 179                :    0.74
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 180                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 181                :    0.16
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 182                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.30
 p-value of test no 183                :    0.10
 
 Sample variance                       :    1.72
 p-value of test no 184                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 185                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 186                :    0.33
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 187                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.23
 p-value of test no 188                :    0.59
 
 Sample variance                       :    2.29
 p-value of test no 189                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:14.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
 p-value of test no 190                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.25
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 192                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
 p-value of test no 193                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :   0.015
 p-value of test no 194                :    0.15
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 195                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   20.72
 p-value of test no 196                :  7.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.90
 p-value of test no 198                :    0.03
 
 -----------------------------------------------
 Global longest run of 1               :   35.00
 p-value of test no 199                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 200                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 201                :    0.81
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 202                :    0.95
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.78
 p-value of test no 203                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 206                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.50
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 208                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.47
 p-value of test no 209                :  7.0e-3
 
 Anderson-Darling statistic = A2       :    2.66
 p-value of test no 210                :    0.04
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10283.62
 p-value of test no 211                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 212                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 213                :    0.92
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 214                :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9783.21
 p-value of test no 215                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 216                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.93
 p-value of test no 217                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 218                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 220                :    0.84
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 221                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4853.47
 p-value of test no 222                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.74
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 224                :    0.21
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 225                :    0.58
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4951.92
 p-value of test no 226                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4255.46
 p-value of test no 227                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4217.00
 p-value of test no 228                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12200.25
 p-value of test no 229                :  7.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11958.89
 p-value of test no 230                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   49.02
 p-value of test no 231                :    0.67
 
 
 -----------------------------------------------
 Total number of bits:  7999999005
 
 Normal statistic for number of bits   : -7.87e-3
 p-value of test no 232                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.49
 p-value of test no 233                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  8000103414
 
 Normal statistic for number of bits   :    0.82
 p-value of test no 234                :    0.21
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 235                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 236                :    0.46
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 237                :    0.95
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.53
 p-value of test no 238                :    0.30
 
 Sample variance                       :    0.93
 p-value of test no 239                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.013
 p-value of test no 240                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.45
 p-value of test no 241                :    0.01
 
 Anderson-Darling statistic = A2       :    4.04
 p-value of test no 242                :  8.7e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    2.69
 p-value of test no 243                :  3.5e-3
 
 Sample variance                       :    0.56
 p-value of test no 244                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.73
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 247                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.41
 p-value of test no 248                :    0.66
 
 Sample variance                       :    1.23
 p-value of test no 249                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 250                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 251                :    0.43
 
 Anderson-Darling statistic = A2       :    0.81
 p-value of test no 252                :    0.47
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.073
 p-value of test no 253                :    0.47
 
 Sample variance                       :    0.49
 p-value of test no 254                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.59
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:41:32.51
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  12  CollisionOver, t = 21           9.4e-4
  24  ClosePairs NJumps, t = 9        6.2e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35991
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 4                  :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:20.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 5                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1354
 p-value of test no 6                  :    0.60
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334474
   j =  1                              :        599997292
   j =  2                              :             1354
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 7                  :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.41
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1422
 p-value of test no 8                  :    0.06
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334542
   j =  1                              :        599997156
   j =  2                              :             1422
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:02.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1438
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334558
   j =  1                              :        599997124
   j =  2                              :             1438
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1337
 p-value of test no 10                 :    0.76
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334457
   j =  1                              :        599997326
   j =  2                              :             1337
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 11                 :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 12                 :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5341
 p-value of test no 13                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4243
 p-value of test no 14                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7392
 p-value of test no 15                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 16                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4416
 p-value of test no 17                 :    0.12
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7273
 p-value of test no 18                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7193
 p-value of test no 19                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7241
 p-value of test no 20                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7397
 p-value of test no 21                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.03
 p-value of test no 22                 :    0.09
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.66
 p-value of test no 23                 :    0.59
 
 Test on the Nm values of W_{n,i}(mNP1):    0.52
 p-value of test no 24                 :    0.73
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    1.05
 p-value of test no 26                 :    0.33
 
 Stat. AD after spacings (mNP2-S)      :    0.54
 p-value of test no 27                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.28
 p-value of test no 28                 :    0.24
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.29
 p-value of test no 29                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.40
 p-value of test no 30                 :    0.84
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     584
 p-value of test no 31                 :    0.74
 
 Stat. AD (mNP2)                       :    2.15
 p-value of test no 32                 :    0.08
 
 Stat. AD after spacings (mNP2-S)      :    0.39
 p-value of test no 33                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.33
 p-value of test no 34                 :    0.91
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.44
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    1.99
 p-value of test no 36                 :    0.09
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     274
 p-value of test no 37                 :    0.93
 
 Stat. AD (mNP2)                       :    0.65
 p-value of test no 38                 :    0.60
 
 Stat. AD after spacings (mNP2-S)      :    2.24
 p-value of test no 39                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:02:07.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 40                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.14
 p-value of test no 41                 :    0.08
 
 Test on the Nm values of W_{n,i}(mNP1):    2.49
 p-value of test no 42                 :    0.05
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     164
 p-value of test no 43                 :    0.14
 
 Stat. AD (mNP2)                       :    1.79
 p-value of test no 44                 :    0.12
 
 Stat. AD after spacings (mNP2-S)      :    0.66
 p-value of test no 45                 :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.49
 p-value of test no 46                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.49
 p-value of test no 47                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   16.58
 p-value of test no 48                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   20.66
 p-value of test no 49                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.11
 p-value of test no 50                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.19
 p-value of test no 51                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   70.35
 p-value of test no 52                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   52.30
 p-value of test no 53                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  255.82
 p-value of test no 54                 :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  389.59
 p-value of test no 55                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1367.63
 p-value of test no 56                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7049.67
 p-value of test no 57                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.093
 p-value of test no 58                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.50
 p-value of test no 59                 :    0.06
 
 Anderson-Darling statistic = A2       :    1.45
 p-value of test no 60                 :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   38.75
 p-value of test no 61                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 63                 :    0.52
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 64                 :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   55.39
 p-value of test no 65                 :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.40
 p-value of test no 66                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :   91.35
 p-value of test no 67                 :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4925.84
 p-value of test no 68                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:59.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46036
 p-value of test no 70                 :    0.23
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870036
   j =  1                              :        399907931
   j =  2                              :            46030
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45742
 p-value of test no 71                 :    0.74
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869742
   j =  1                              :        399908518
   j =  2                              :            45738
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.71e-4
 p-value of test no 72                 :    0.9992    *****
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 73                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.36
 p-value of test no 74                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.01e+6
 p-value of test no 75                 :    0.01
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.029
 p-value of test no 77                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 78                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 79                 :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 80                 :    0.53
 
 Anderson-Darling statistic = A2       :    0.94
 p-value of test no 81                 :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 83                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 84                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.62
 p-value of test no 85                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 86                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 87                 :    0.13
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 88                 :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.16
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 90                 :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :   0.049
 p-value of test no 91                 :    0.88
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 92                 :    0.92
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.084
 p-value of test no 93                 :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 94                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 95                 :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.29
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
 p-value of test no 97                 :    0.9916
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 98                 :    0.05
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 99                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.083
 p-value of test no 100                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 101                :    0.35
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 102                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 103                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 104                :    0.16
 
 Anderson-Darling statistic = A2       :    1.09
 p-value of test no 105                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 106                :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 107                :    0.41
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 108                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
 p-value of test no 109                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
 p-value of test no 110                :    0.53
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 111                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:18.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
 p-value of test no 112                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
 p-value of test no 113                :    0.50
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.76
 p-value of test no 117                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.74
 p-value of test no 118                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.24
 p-value of test no 119                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.39
 p-value of test no 120                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   67.28
 p-value of test no 121                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.18
 p-value of test no 122                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.54
 p-value of test no 123                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.60
 p-value of test no 124                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   47.19
 p-value of test no 125                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 127                :    0.28
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 128                :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   45.29
 p-value of test no 129                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.44
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 132                :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.27
 p-value of test no 133                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.89
 p-value of test no 134                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.10
 p-value of test no 135                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.51
 p-value of test no 136                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.27
 p-value of test no 137                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 138                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 139                :    0.10
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 140                :    0.23
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  129.45
 p-value of test no 141                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.076
 p-value of test no 142                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 143                :    0.03
 
 Anderson-Darling statistic = A2       :    1.47
 p-value of test no 144                :    0.18
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17661.49
 p-value of test no 145                :    0.11
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   27.07
 p-value of test no 146                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.56
 p-value of test no 147                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   22.78
 p-value of test no 148                :    0.59
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.63
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.01
 p-value of test no 150                :    0.27
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.04
 p-value of test no 151                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.97
 p-value of test no 152                :    0.22
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   26.60
 p-value of test no 153                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   35.78
 p-value of test no 154                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.45
 p-value of test no 155                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  146.66
 p-value of test no 156                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.55
 p-value of test no 157                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  479.96
 p-value of test no 158                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.11
 p-value of test no 159                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.99
 p-value of test no 160                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.99
 p-value of test no 161                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.11
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  505.00
 p-value of test no 163                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.75
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.98
 p-value of test no 165                :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  405.63
 p-value of test no 166                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.80
 p-value of test no 167                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5091.60
 p-value of test no 168                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  346.47
 p-value of test no 169                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.01
 p-value of test no 170                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  415.65
 p-value of test no 171                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  374.10
 p-value of test no 172                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5054.73
 p-value of test no 173                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.37
 p-value of test no 174                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  203.72
 p-value of test no 175                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.70
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.90
 p-value of test no 177                :    0.97
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   14.07
 p-value of test no 178                :    0.30
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.78
 p-value of test no 179                :    0.78
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.067
 p-value of test no 180                :    0.88
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 181                :    0.27
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 182                :    0.61
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.76
 p-value of test no 183                :    0.23
 
 Sample variance                       :    0.92
 p-value of test no 184                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 185                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 187                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.47
 p-value of test no 188                :    0.32
 
 Sample variance                       :    0.84
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:03.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
 p-value of test no 191                :    0.46
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 192                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
 p-value of test no 193                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
 p-value of test no 194                :    0.77
 
 Anderson-Darling statistic = A2       :    0.26
 p-value of test no 195                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.98
 p-value of test no 196                :    0.76
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.97
 p-value of test no 198                :    0.86
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 199                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.36
 p-value of test no 200                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 201                :    0.67
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 202                :    0.19
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  176.85
 p-value of test no 203                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:57.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 205                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  205.35
 p-value of test no 207                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 208                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 209                :    0.10
 
 Anderson-Darling statistic = A2       :    1.67
 p-value of test no 210                :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10244.49
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 213                :    0.15
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 214                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10095.83
 p-value of test no 215                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.28
 p-value of test no 216                :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.50
 p-value of test no 217                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.13
 p-value of test no 218                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.026
 p-value of test no 220                :    0.97
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 221                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4795.21
 p-value of test no 222                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 223                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 225                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4891.59
 p-value of test no 226                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4075.73
 p-value of test no 227                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4238.25
 p-value of test no 228                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11898.98
 p-value of test no 229                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :12023.06
 p-value of test no 230                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   59.93
 p-value of test no 231                :    0.27
 
 
 -----------------------------------------------
 Total number of bits:  7999911729
 
 Normal statistic for number of bits   :   -0.70
 p-value of test no 232                :    0.76
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   39.63
 p-value of test no 233                :    0.93
 
 
 -----------------------------------------------
 Total number of bits:  7999971399
 
 Normal statistic for number of bits   :   -0.23
 p-value of test no 234                :    0.59
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 235                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 236                :    0.40
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 237                :    0.85
 
 Tests on the sum of all N observations
 Standardized normal statistic         : 8.62e-3
 p-value of test no 238                :    0.50
 
 Sample variance                       :    0.64
 p-value of test no 239                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 240                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 241                :    0.04
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 242                :    0.09
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.44
 p-value of test no 243                :    0.07
 
 Sample variance                       :    0.83
 p-value of test no 244                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 246                :    0.50
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 247                :    0.64
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.31
 p-value of test no 248                :    0.38
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 250                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.35
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 252                :    0.86
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.18
 p-value of test no 253                :    0.43
 
 Sample variance                       :    1.29
 p-value of test no 254                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:36.12
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35992
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.9907
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1340
 p-value of test no 3                  :    0.74
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334460
   j =  1                              :        599997320
   j =  2                              :             1340
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:00.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1342
 p-value of test no 4                  :    0.72
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334462
   j =  1                              :        599997316
   j =  2                              :             1342
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:17.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1441
 p-value of test no 5                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334561
   j =  1                              :        599997118
   j =  2                              :             1441
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1442
 p-value of test no 6                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334562
   j =  1                              :        599997116
   j =  2                              :             1442
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1433
 p-value of test no 7                  :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334553
   j =  1                              :        599997134
   j =  2                              :             1433
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1367
 p-value of test no 8                  :    0.47
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334487
   j =  1                              :        599997266
   j =  2                              :             1367
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1285
 p-value of test no 10                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334405
   j =  1                              :        599997430
   j =  2                              :             1285
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1365
 p-value of test no 11                 :    0.50
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334485
   j =  1                              :        599997270
   j =  2                              :             1365
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:35.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 12                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5434
 p-value of test no 13                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4332
 p-value of test no 14                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7311
 p-value of test no 15                 :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4308
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4224
 p-value of test no 17                 :    0.96
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7232
 p-value of test no 18                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 19                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7326
 p-value of test no 20                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7414
 p-value of test no 21                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.16
 p-value of test no 22                 :    0.28
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.15
 p-value of test no 23                 :    0.29
 
 Test on the Nm values of W_{n,i}(mNP1):    0.68
 p-value of test no 24                 :    0.58
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     866
 p-value of test no 25                 :    0.87
 
 Stat. AD (mNP2)                       :    1.55
 p-value of test no 26                 :    0.16
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 27                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.42
 p-value of test no 28                 :    0.83
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 29                 :    0.77
 
 Test on the Nm values of W_{n,i}(mNP1):    0.37
 p-value of test no 30                 :    0.88
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     591
 p-value of test no 31                 :    0.63
 
 Stat. AD (mNP2)                       :    1.38
 p-value of test no 32                 :    0.21
 
 Stat. AD after spacings (mNP2-S)      :    0.51
 p-value of test no 33                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.57
 p-value of test no 34                 :    0.67
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.80
 p-value of test no 35                 :    0.48
 
 Test on the Nm values of W_{n,i}(mNP1):    1.26
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     276
 p-value of test no 37                 :    0.91
 
 Stat. AD (mNP2)                       :    0.42
 p-value of test no 38                 :    0.83
 
 Stat. AD after spacings (mNP2-S)      :    0.97
 p-value of test no 39                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    2.13
 p-value of test no 40                 :    0.08
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.39
 p-value of test no 41                 :    0.86
 
 Test on the Nm values of W_{n,i}(mNP1):    0.60
 p-value of test no 42                 :    0.65
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     135
 p-value of test no 43                 :    0.88
 
 Stat. AD (mNP2)                       :    1.47
 p-value of test no 44                 :    0.18
 
 Stat. AD after spacings (mNP2-S)      :    0.37
 p-value of test no 45                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.27
 p-value of test no 46                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    2.86
 p-value of test no 47                 :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :    9.72
 p-value of test no 48                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.45
 p-value of test no 49                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.72
 p-value of test no 50                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.54
 p-value of test no 51                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.13
 p-value of test no 52                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   32.01
 p-value of test no 53                 :    0.9925
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  208.23
 p-value of test no 54                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  437.91
 p-value of test no 55                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1504.69
 p-value of test no 56                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7020.93
 p-value of test no 57                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 58                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 59                 :    0.49
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 60                 :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   27.16
 p-value of test no 61                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.074
 p-value of test no 62                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 63                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 64                 :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   70.21
 p-value of test no 65                 :    0.17
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.70
 p-value of test no 66                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  111.29
 p-value of test no 67                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5168.07
 p-value of test no 68                 :    0.10
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:57.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45450
 p-value of test no 70                 :    0.98
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869450
   j =  1                              :        399909106
   j =  2                              :            45438
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45863
 p-value of test no 71                 :    0.53
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869863
   j =  1                              :        399908282
   j =  2                              :            45847
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 72                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 73                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.63
 p-value of test no 74                 :    0.62
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.28
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 76                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 77                 :    0.22
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 78                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.059
 p-value of test no 79                 :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 80                 :    0.25
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 81                 :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.23
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.063
 p-value of test no 83                 :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 85                 :    0.43
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 86                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 87                 :    0.05
 
 Anderson-Darling statistic = A2       :    1.76
 p-value of test no 88                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 91                 :    0.58
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 92                 :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 95                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 97                 :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 98                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 99                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 100                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.061
 p-value of test no 101                :    0.71
 
 Anderson-Darling statistic = A2       :    1.77
 p-value of test no 102                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.020
 p-value of test no 103                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 104                :    0.06
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 106                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 108                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
 p-value of test no 109                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
 p-value of test no 110                :    0.30
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 111                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
 p-value of test no 112                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    : 4.25e-5
 p-value of test no 113                :    0.93
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 114                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.28
 p-value of test no 115                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.66
 p-value of test no 116                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.37
 p-value of test no 117                :    0.9910
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.89
 p-value of test no 118                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   58.56
 p-value of test no 119                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   64.93
 p-value of test no 120                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   63.98
 p-value of test no 121                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   43.59
 p-value of test no 122                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.81
 p-value of test no 123                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   36.89
 p-value of test no 124                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   33.80
 p-value of test no 125                :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 126                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.33
 p-value of test no 127                :    0.09
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.66
 p-value of test no 129                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 130                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.092
 p-value of test no 131                :    0.80
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 132                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.60
 p-value of test no 133                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.53
 p-value of test no 134                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.22
 p-value of test no 135                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :   0.059
 p-value of test no 136                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.36
 p-value of test no 137                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 139                :    0.53
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 140                :    0.84
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  136.17
 p-value of test no 141                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.65
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 144                :    0.66
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17347.24
 p-value of test no 145                :    0.67
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   48.26
 p-value of test no 146                :    0.08
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.63
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   16.09
 p-value of test no 148                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.65
 p-value of test no 149                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   21.18
 p-value of test no 150                :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.16
 p-value of test no 151                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.22
 p-value of test no 152                :    0.78
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   24.17
 p-value of test no 153                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.41
 p-value of test no 154                :    0.44
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   14.55
 p-value of test no 155                :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  151.26
 p-value of test no 156                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.95
 p-value of test no 157                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.89
 p-value of test no 158                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  117.41
 p-value of test no 159                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   84.34
 p-value of test no 160                :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  160.53
 p-value of test no 161                :    0.19
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.70
 p-value of test no 162                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  542.68
 p-value of test no 163                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  191.93
 p-value of test no 164                :  1.1e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   86.98
 p-value of test no 165                :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.79
 p-value of test no 166                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  412.20
 p-value of test no 167                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5105.12
 p-value of test no 168                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.31
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  201.08
 p-value of test no 170                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  410.24
 p-value of test no 171                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  399.13
 p-value of test no 172                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4964.44
 p-value of test no 173                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  333.48
 p-value of test no 174                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  208.76
 p-value of test no 175                :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    9.27
 p-value of test no 176                :    0.68
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.51
 p-value of test no 177                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.21
 p-value of test no 178                :    0.84
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 180                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 181                :    0.34
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.34
 p-value of test no 183                :    0.09
 
 Sample variance                       :    1.24
 p-value of test no 184                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 185                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 186                :    0.64
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.90
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.011
 p-value of test no 188                :    0.50
 
 Sample variance                       :    0.57
 p-value of test no 189                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
 p-value of test no 191                :    0.65
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 192                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 193                :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 194                :    0.33
 
 Anderson-Darling statistic = A2       :    1.78
 p-value of test no 195                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    7.19
 p-value of test no 196                :    0.52
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.73
 p-value of test no 198                :    0.68
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 200                :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 201                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 202                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.21
 p-value of test no 203                :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:56.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 205                :    0.28
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 206                :    0.57
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  210.16
 p-value of test no 207                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 208                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 209                :    0.72
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 210                :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9931.55
 p-value of test no 211                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 212                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :   0.100
 p-value of test no 213                :    0.77
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 214                :    0.71
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9911.47
 p-value of test no 215                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.76
 p-value of test no 216                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.55
 p-value of test no 217                :    0.9947
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.91
 p-value of test no 218                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 219                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 220                :    0.56
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 221                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4926.56
 p-value of test no 222                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.016
 p-value of test no 223                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.38
 p-value of test no 224                :    0.04
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 225                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5089.17
 p-value of test no 226                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4086.83
 p-value of test no 227                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4052.46
 p-value of test no 228                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11731.96
 p-value of test no 229                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11770.04
 p-value of test no 230                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   58.48
 p-value of test no 231                :    0.31
 
 
 -----------------------------------------------
 Total number of bits:  7999956102
 
 Normal statistic for number of bits   :   -0.35
 p-value of test no 232                :    0.64
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.79
 p-value of test no 233                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  8000053197
 
 Normal statistic for number of bits   :    0.42
 p-value of test no 234                :    0.34
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 235                :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.037
 p-value of test no 236                :    0.95
 
 Anderson-Darling statistic = A2       :    1.92
 p-value of test no 237                :    0.10
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.86
 p-value of test no 238                :    0.97
 
 Sample variance                       :    0.72
 p-value of test no 239                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.58
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 242                :    0.87
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.35
 p-value of test no 243                :    0.64
 
 Sample variance                       :    0.84
 p-value of test no 244                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 245                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 246                :    0.35
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 247                :    0.63
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.64
 p-value of test no 248                :    0.26
 
 Sample variance                       :    0.72
 p-value of test no 249                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.04
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 251                :    0.91
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.65
 p-value of test no 253                :    0.74
 
 Sample variance                       :    0.90
 p-value of test no 254                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.63
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:18.29
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35993
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.97
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1414
 p-value of test no 3                  :    0.09
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334534
   j =  1                              :        599997172
   j =  2                              :             1414
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:58.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1356
 p-value of test no 4                  :    0.58
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334476
   j =  1                              :        599997288
   j =  2                              :             1356
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:14.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1299
 p-value of test no 5                  :    0.96
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334419
   j =  1                              :        599997402
   j =  2                              :             1299
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 6                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 7                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1413
 p-value of test no 8                  :    0.10
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334533
   j =  1                              :        599997174
   j =  2                              :             1413
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1443
 p-value of test no 9                  :    0.02
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334563
   j =  1                              :        599997114
   j =  2                              :             1443
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1405
 p-value of test no 10                 :    0.14
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334525
   j =  1                              :        599997190
   j =  2                              :             1405
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:04.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1239
 p-value of test no 11                 :    0.9997    *****
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334359
   j =  1                              :        599997522
   j =  2                              :             1239
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1290
 p-value of test no 12                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334410
   j =  1                              :        599997420
   j =  2                              :             1290
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5453
 p-value of test no 13                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4387
 p-value of test no 14                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4336
 p-value of test no 16                 :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4388
 p-value of test no 17                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7310
 p-value of test no 18                 :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7262
 p-value of test no 19                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7341
 p-value of test no 20                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7279
 p-value of test no 21                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.84
 p-value of test no 22                 :    0.45
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.27
 p-value of test no 23                 :    0.24
 
 Test on the Nm values of W_{n,i}(mNP1):    0.83
 p-value of test no 24                 :    0.46
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     898
 p-value of test no 25                 :    0.52
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 26                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    2.03
 p-value of test no 27                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.31
 p-value of test no 28                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 29                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    1.41
 p-value of test no 30                 :    0.20
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     594
 p-value of test no 31                 :    0.59
 
 Stat. AD (mNP2)                       :    0.25
 p-value of test no 32                 :    0.97
 
 Stat. AD after spacings (mNP2-S)      :    0.70
 p-value of test no 33                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.96
 p-value of test no 34                 :    0.38
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.94
 p-value of test no 35                 :    0.10
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 36                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     305
 p-value of test no 37                 :    0.39
 
 Stat. AD (mNP2)                       :    0.44
 p-value of test no 38                 :    0.81
 
 Stat. AD after spacings (mNP2-S)      :    2.65
 p-value of test no 39                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    4.64
 p-value of test no 40                 :  4.7e-3
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.56
 p-value of test no 41                 :    0.68
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     146
 p-value of test no 43                 :    0.61
 
 Stat. AD (mNP2)                       :    0.71
 p-value of test no 44                 :    0.55
 
 Stat. AD after spacings (mNP2-S)      :    0.83
 p-value of test no 45                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :   12.17
 p-value of test no 46                 :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.67
 p-value of test no 47                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   22.06
 p-value of test no 48                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.93
 p-value of test no 49                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.36
 p-value of test no 50                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.31
 p-value of test no 51                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.94
 p-value of test no 52                 :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   53.23
 p-value of test no 53                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.20
 p-value of test no 54                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  433.09
 p-value of test no 55                 :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1445.64
 p-value of test no 56                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7237.77
 p-value of test no 57                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 58                 :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :    0.39
 p-value of test no 59                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 60                 :    0.47
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   30.04
 p-value of test no 61                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 62                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 63                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 64                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   65.05
 p-value of test no 65                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    5.87
 p-value of test no 66                 :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  100.94
 p-value of test no 67                 :    0.88
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5060.69
 p-value of test no 68                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46017
 p-value of test no 70                 :    0.26
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870017
   j =  1                              :        399907968
   j =  2                              :            46013
   j =  3                              :                2
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46208
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870208
   j =  1                              :        399907589
   j =  2                              :            46198
   j =  3                              :                5
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 72                 :    0.77
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 73                 :    0.18
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 74                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.24
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.022
 p-value of test no 77                 :    0.95
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 78                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 79                 :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :   0.040
 p-value of test no 80                 :    0.89
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 81                 :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.85
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.055
 p-value of test no 83                 :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :   0.082
 p-value of test no 84                 :    0.64
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 85                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 86                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 87                 :    0.89
 
 Anderson-Darling statistic = A2       :    2.01
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.95
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.023
 p-value of test no 90                 :    0.96
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 91                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.32
 p-value of test no 92                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 94                 :    0.14
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 95                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.44
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 97                 :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 98                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 99                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
 p-value of test no 100                :    0.9911
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 103                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 104                :    0.89
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 105                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.064
 p-value of test no 106                :    0.81
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.22
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 108                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
 p-value of test no 109                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.93e-5
 p-value of test no 112                :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
 p-value of test no 113                :    0.13
 
 Anderson-Darling statistic = A2       :    1.05
 p-value of test no 114                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.11
 p-value of test no 115                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.12
 p-value of test no 116                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.47
 p-value of test no 117                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.55
 p-value of test no 118                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   55.97
 p-value of test no 119                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   79.62
 p-value of test no 120                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   84.93
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.30
 p-value of test no 122                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   31.19
 p-value of test no 123                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   22.67
 p-value of test no 124                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   34.91
 p-value of test no 125                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 126                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.52
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 128                :    0.69
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   39.14
 p-value of test no 129                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 130                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 131                :    0.87
 
 Anderson-Darling statistic = A2       :    1.52
 p-value of test no 132                :    0.17
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   33.89
 p-value of test no 133                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.16
 p-value of test no 134                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   0.048
 p-value of test no 135                :    0.9973
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.40
 p-value of test no 136                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    6.35
 p-value of test no 137                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 138                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 139                :    0.12
 
 Anderson-Darling statistic = A2       :    2.02
 p-value of test no 140                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  161.43
 p-value of test no 141                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 142                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 143                :    0.87
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 144                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17247.94
 p-value of test no 145                :    0.84
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   45.27
 p-value of test no 146                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   37.16
 p-value of test no 147                :    0.37
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.38
 p-value of test no 148                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.76
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   27.26
 p-value of test no 150                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.25
 p-value of test no 151                :    0.69
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.46
 p-value of test no 152                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   13.12
 p-value of test no 153                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.64
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   19.49
 p-value of test no 155                :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  176.90
 p-value of test no 156                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  177.23
 p-value of test no 157                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  461.40
 p-value of test no 158                :    0.89
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  158.60
 p-value of test no 159                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   70.48
 p-value of test no 160                :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  135.74
 p-value of test no 161                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  141.77
 p-value of test no 162                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  559.61
 p-value of test no 163                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.50
 p-value of test no 164                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   95.33
 p-value of test no 165                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  333.78
 p-value of test no 166                :    0.97
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.68
 p-value of test no 167                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5058.59
 p-value of test no 168                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  425.81
 p-value of test no 169                :    0.05
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  234.20
 p-value of test no 170                :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  385.28
 p-value of test no 171                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  373.14
 p-value of test no 172                :    0.64
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4987.35
 p-value of test no 173                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  383.20
 p-value of test no 174                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  204.51
 p-value of test no 175                :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.65
 p-value of test no 176                :    0.32
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -2.54
 p-value of test no 177                :    0.9945
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   15.30
 p-value of test no 178                :    0.23
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.72
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.27
 p-value of test no 180                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 181                :    0.69
 
 Anderson-Darling statistic = A2       :    0.87
 p-value of test no 182                :    0.43
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.82
 p-value of test no 183                :    0.79
 
 Sample variance                       :    0.46
 p-value of test no 184                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 185                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.50
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 187                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.14
 p-value of test no 188                :    0.55
 
 Sample variance                       :    0.32
 p-value of test no 189                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 190                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 191                :    0.11
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 192                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 193                :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
 p-value of test no 194                :    0.75
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 195                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.84
 p-value of test no 196                :    0.16
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   14.50
 p-value of test no 198                :    0.07
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.58
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 201                :    0.42
 
 Anderson-Darling statistic = A2       :    0.39
 p-value of test no 202                :    0.86
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.15
 p-value of test no 203                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 204                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.60
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 206                :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  207.29
 p-value of test no 207                :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 209                :    0.67
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 210                :    0.80
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9988.61
 p-value of test no 211                :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 212                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 213                :    0.41
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10033.29
 p-value of test no 215                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.56
 p-value of test no 216                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    2.41
 p-value of test no 217                :  8.1e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.98
 p-value of test no 218                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 219                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 220                :    0.42
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 221                :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4936.35
 p-value of test no 222                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 223                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 224                :    0.32
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 225                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4920.15
 p-value of test no 226                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4184.58
 p-value of test no 227                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4107.23
 p-value of test no 228                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11794.04
 p-value of test no 229                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11933.16
 p-value of test no 230                :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.61
 p-value of test no 231                :    0.38
 
 
 -----------------------------------------------
 Total number of bits:  8000065881
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 232                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   51.00
 p-value of test no 233                :    0.59
 
 
 -----------------------------------------------
 Total number of bits:  8000119266
 
 Normal statistic for number of bits   :    0.94
 p-value of test no 234                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 235                :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 236                :    0.29
 
 Anderson-Darling statistic = A2       :    2.24
 p-value of test no 237                :    0.07
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.78
 p-value of test no 238                :    0.78
 
 Sample variance                       :    2.30
 p-value of test no 239                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 240                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    :   0.069
 p-value of test no 241                :    0.87
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 242                :    0.97
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.38
 p-value of test no 243                :    0.65
 
 Sample variance                       :    1.21
 p-value of test no 244                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 245                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 246                :    0.56
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 247                :    0.42
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    1.40
 p-value of test no 249                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 251                :    0.55
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 252                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 253                :    0.46
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:05.95
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  11  CollisionOver, t = 21           0.9997 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35994
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.31
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 3                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:55.08
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 4                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1398
 p-value of test no 5                  :    0.18
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334518
   j =  1                              :        599997204
   j =  2                              :             1398
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 6                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.83
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1403
 p-value of test no 7                  :    0.15
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334523
   j =  1                              :        599997194
   j =  2                              :             1403
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1331
 p-value of test no 8                  :    0.81
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334451
   j =  1                              :        599997338
   j =  2                              :             1331
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1349
 p-value of test no 9                  :    0.65
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334469
   j =  1                              :        599997302
   j =  2                              :             1349
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1351
 p-value of test no 10                 :    0.63
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334471
   j =  1                              :        599997298
   j =  2                              :             1351
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 11                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1417
 p-value of test no 12                 :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334537
   j =  1                              :        599997166
   j =  2                              :             1417
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5446
 p-value of test no 13                 :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4305
 p-value of test no 14                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7289
 p-value of test no 15                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4399
 p-value of test no 16                 :    0.17
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4257
 p-value of test no 17                 :    0.89
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7403
 p-value of test no 18                 :    0.16
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7363
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7264
 p-value of test no 20                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7475
 p-value of test no 21                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.40
 p-value of test no 22                 :    0.85
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.32
 p-value of test no 23                 :    0.92
 
 Test on the Nm values of W_{n,i}(mNP1):    4.43
 p-value of test no 24                 :  5.4e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     839
 p-value of test no 25                 :    0.98
 
 Stat. AD (mNP2)                       :    0.85
 p-value of test no 26                 :    0.44
 
 Stat. AD after spacings (mNP2-S)      :    1.09
 p-value of test no 27                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.74
 p-value of test no 28                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.75
 p-value of test no 29                 :    0.51
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 30                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     585
 p-value of test no 31                 :    0.72
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    0.95
 p-value of test no 33                 :    0.39
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.53
 p-value of test no 34                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.96
 p-value of test no 35                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    1.28
 p-value of test no 36                 :    0.24
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     280
 p-value of test no 37                 :    0.87
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 38                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    1.01
 p-value of test no 39                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.58
 p-value of test no 40                 :    0.66
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.42
 p-value of test no 41                 :    0.83
 
 Test on the Nm values of W_{n,i}(mNP1):    0.91
 p-value of test no 42                 :    0.41
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.98
 p-value of test no 44                 :    0.37
 
 Stat. AD after spacings (mNP2-S)      :    0.56
 p-value of test no 45                 :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:02:33.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    1.29
 p-value of test no 46                 :    0.99
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    8.20
 p-value of test no 47                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.30
 p-value of test no 48                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   12.76
 p-value of test no 49                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.76
 p-value of test no 50                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:45.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.97
 p-value of test no 51                 :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   56.63
 p-value of test no 52                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   55.28
 p-value of test no 53                 :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  220.49
 p-value of test no 54                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  419.14
 p-value of test no 55                 :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1552.58
 p-value of test no 56                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6790.91
 p-value of test no 57                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 58                 :    0.34
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 59                 :    0.85
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 60                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   24.69
 p-value of test no 61                 :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 62                 :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.083
 p-value of test no 63                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 64                 :    0.94
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   58.27
 p-value of test no 65                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.96
 p-value of test no 66                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  130.54
 p-value of test no 67                 :    0.22
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4952.67
 p-value of test no 68                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:51.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45631
 p-value of test no 70                 :    0.88
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869631
   j =  1                              :        399908741
   j =  2                              :            45625
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46140
 p-value of test no 71                 :    0.11
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870140
   j =  1                              :        399907723
   j =  2                              :            46134
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 72                 :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 73                 :    0.83
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 74                 :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.63
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 76                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :   0.093
 p-value of test no 77                 :    0.47
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 78                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 79                 :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.078
 p-value of test no 80                 :    0.66
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 81                 :    0.67
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.64
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 83                 :    0.12
 
 Kolmogorov-Smirnov- statistic = D-    :   0.055
 p-value of test no 84                 :    0.80
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 85                 :    0.59
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 86                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 87                 :    0.32
 
 Anderson-Darling statistic = A2       :    0.71
 p-value of test no 88                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 90                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 91                 :    0.90
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 92                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 94                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 95                 :    0.55
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.48
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 97                 :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.53
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 99                 :    0.20
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.021
 p-value of test no 100                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 101                :    0.06
 
 Anderson-Darling statistic = A2       :    2.17
 p-value of test no 102                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 104                :    0.68
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 105                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 106                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 107                :    0.20
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 108                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
 p-value of test no 109                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
 p-value of test no 110                :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 111                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
 p-value of test no 112                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.43
 
 Anderson-Darling statistic = A2       :    0.30
 p-value of test no 114                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.84
 p-value of test no 115                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   0.030
 p-value of test no 116                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.06
 p-value of test no 117                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.75
 p-value of test no 118                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   50.52
 p-value of test no 119                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   69.88
 p-value of test no 120                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.55
 p-value of test no 121                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   41.87
 p-value of test no 122                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.68
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   39.44
 p-value of test no 124                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.51
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
 p-value of test no 126                :    0.9943
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 127                :    0.02
 
 Anderson-Darling statistic = A2       :    2.55
 p-value of test no 128                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   62.89
 p-value of test no 129                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 131                :    0.72
 
 Anderson-Darling statistic = A2       :    0.74
 p-value of test no 132                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   30.10
 p-value of test no 133                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    3.42
 p-value of test no 134                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.43
 p-value of test no 135                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.32
 p-value of test no 136                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.37
 p-value of test no 137                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 138                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.070
 p-value of test no 139                :    0.87
 
 Anderson-Darling statistic = A2       :    0.89
 p-value of test no 140                :    0.42
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  113.17
 p-value of test no 141                :    0.85
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 142                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 143                :    0.33
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 144                :    0.32
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17632.05
 p-value of test no 145                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   28.88
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   21.57
 p-value of test no 147                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.68
 p-value of test no 148                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.68
 p-value of test no 149                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   13.28
 p-value of test no 150                :    0.72
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.48
 p-value of test no 151                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.58
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.59
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   15.17
 p-value of test no 154                :    0.92
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   10.12
 p-value of test no 155                :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  164.05
 p-value of test no 156                :    0.15
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  128.53
 p-value of test no 157                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  470.68
 p-value of test no 158                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  155.32
 p-value of test no 159                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   76.10
 p-value of test no 160                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  134.14
 p-value of test no 161                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.01
 p-value of test no 162                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  502.43
 p-value of test no 163                :    0.46
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  126.02
 p-value of test no 164                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   81.20
 p-value of test no 165                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  368.22
 p-value of test no 166                :    0.71
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  367.09
 p-value of test no 167                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5026.84
 p-value of test no 168                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  373.37
 p-value of test no 169                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  206.53
 p-value of test no 170                :    0.36
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  365.03
 p-value of test no 171                :    0.75
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  351.17
 p-value of test no 172                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5003.24
 p-value of test no 173                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  364.68
 p-value of test no 174                :    0.68
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  231.31
 p-value of test no 175                :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.45
 p-value of test no 176                :    0.13
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.32
 p-value of test no 177                :    0.09
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.53
 p-value of test no 178                :    0.33
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.74
 p-value of test no 179                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 180                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 181                :    0.40
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 182                :    0.60
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.56
 p-value of test no 183                :    0.29
 
 Sample variance                       :    1.61
 p-value of test no 184                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 185                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 186                :    0.16
 
 Anderson-Darling statistic = A2       :    1.31
 p-value of test no 187                :    0.23
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.85
 p-value of test no 188                :    0.20
 
 Sample variance                       :    1.62
 p-value of test no 189                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
 p-value of test no 190                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
 p-value of test no 191                :    0.70
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 192                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
 p-value of test no 193                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
 p-value of test no 194                :    0.78
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 195                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   11.27
 p-value of test no 196                :    0.19
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   16.37
 p-value of test no 198                :    0.04
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 199                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 200                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 201                :    0.84
 
 Anderson-Darling statistic = A2       :    0.82
 p-value of test no 202                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.72
 p-value of test no 203                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 204                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 205                :    0.63
 
 Anderson-Darling statistic = A2       :    0.52
 p-value of test no 206                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.71
 p-value of test no 207                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 208                :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.22
 
 Anderson-Darling statistic = A2       :    0.93
 p-value of test no 210                :    0.39
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10104.94
 p-value of test no 211                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 212                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 213                :    0.59
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 214                :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10007.02
 p-value of test no 215                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.09
 p-value of test no 216                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.78
 p-value of test no 217                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.44
 p-value of test no 218                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 219                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.074
 p-value of test no 220                :    0.86
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 221                :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4831.37
 p-value of test no 222                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.37
 p-value of test no 223                :    0.05
 
 Kolmogorov-Smirnov- statistic = D-    :   0.066
 p-value of test no 224                :    0.88
 
 Anderson-Darling statistic = A2       :    1.37
 p-value of test no 225                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4772.57
 p-value of test no 226                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4006.26
 p-value of test no 227                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4205.75
 p-value of test no 228                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11633.85
 p-value of test no 229                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11581.19
 p-value of test no 230                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.90
 p-value of test no 231                :    0.48
 
 
 -----------------------------------------------
 Total number of bits:  7999939923
 
 Normal statistic for number of bits   :   -0.47
 p-value of test no 232                :    0.68
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   57.74
 p-value of test no 233                :    0.34
 
 
 -----------------------------------------------
 Total number of bits:  7999905021
 
 Normal statistic for number of bits   :   -0.75
 p-value of test no 234                :    0.77
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.46
 p-value of test no 235                :  9.4e-3
 
 Kolmogorov-Smirnov- statistic = D-    : 5.06e-4
 p-value of test no 236                :    0.9995    *****
 
 Anderson-Darling statistic = A2       :    4.54
 p-value of test no 237                :  5.0e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -3.12
 p-value of test no 238                :    0.9991    *****
 
 Sample variance                       :    1.48
 p-value of test no 239                :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.052
 p-value of test no 240                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.23
 p-value of test no 241                :    0.31
 
 Anderson-Darling statistic = A2       :    0.72
 p-value of test no 242                :    0.54
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.97
 p-value of test no 243                :    0.17
 
 Sample variance                       :    0.59
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.22
 p-value of test no 245                :    0.33
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 246                :    0.84
 
 Anderson-Darling statistic = A2       :    0.59
 p-value of test no 247                :    0.65
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.68
 p-value of test no 248                :    0.75
 
 Sample variance                       :    0.67
 p-value of test no 249                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.019
 p-value of test no 250                :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 251                :    0.21
 
 Anderson-Darling statistic = A2       :    1.63
 p-value of test no 252                :    0.15
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.69
 p-value of test no 253                :    0.05
 
 Sample variance                       :    1.35
 p-value of test no 254                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.73
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.07
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  103  AutoCor, d=1, r=0               0.9991 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35995
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.21
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1359
 p-value of test no 3                  :    0.55
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334479
   j =  1                              :        599997282
   j =  2                              :             1359
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1332
 p-value of test no 4                  :    0.80
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334452
   j =  1                              :        599997336
   j =  2                              :             1332
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1431
 p-value of test no 5                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334551
   j =  1                              :        599997138
   j =  2                              :             1431
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1416
 p-value of test no 6                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334536
   j =  1                              :        599997168
   j =  2                              :             1416
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.33
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1402
 p-value of test no 7                  :    0.16
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334522
   j =  1                              :        599997196
   j =  2                              :             1402
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1326
 p-value of test no 8                  :    0.85
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334446
   j =  1                              :        599997348
   j =  2                              :             1326
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:06.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1373
 p-value of test no 9                  :    0.41
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334493
   j =  1                              :        599997254
   j =  2                              :             1373
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:59.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1429
 p-value of test no 11                 :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334549
   j =  1                              :        599997142
   j =  2                              :             1429
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1386
 p-value of test no 12                 :    0.28
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334506
   j =  1                              :        599997228
   j =  2                              :             1386
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:44.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5297
 p-value of test no 13                 :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:33.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4238
 p-value of test no 14                 :    0.93
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7245
 p-value of test no 15                 :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4307
 p-value of test no 16                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4398
 p-value of test no 17                 :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 18                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7282
 p-value of test no 19                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7233
 p-value of test no 20                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7220
 p-value of test no 21                 :    0.87
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.71
 p-value of test no 22                 :    0.55
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    2.49
 p-value of test no 23                 :    0.05
 
 Test on the Nm values of W_{n,i}(mNP1):    0.80
 p-value of test no 24                 :    0.48
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     884
 p-value of test no 25                 :    0.70
 
 Stat. AD (mNP2)                       :    0.73
 p-value of test no 26                 :    0.53
 
 Stat. AD after spacings (mNP2-S)      :    2.64
 p-value of test no 27                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.43
 p-value of test no 28                 :    0.81
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.22
 p-value of test no 29                 :    0.99
 
 Test on the Nm values of W_{n,i}(mNP1):    1.76
 p-value of test no 30                 :    0.12
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     589
 p-value of test no 31                 :    0.66
 
 Stat. AD (mNP2)                       :    0.81
 p-value of test no 32                 :    0.47
 
 Stat. AD after spacings (mNP2-S)      :    0.81
 p-value of test no 33                 :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.65
 p-value of test no 34                 :    0.60
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.43
 p-value of test no 35                 :    0.81
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     319
 p-value of test no 37                 :    0.14
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 38                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.18
 p-value of test no 39                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.51
 p-value of test no 40                 :    0.17
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.97
 p-value of test no 41                 :    0.37
 
 Test on the Nm values of W_{n,i}(mNP1):    0.26
 p-value of test no 42                 :    0.97
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     149
 p-value of test no 43                 :    0.51
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 44                 :    0.88
 
 Stat. AD after spacings (mNP2-S)      :    1.36
 p-value of test no 45                 :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.23
 p-value of test no 46                 :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.11
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.74
 p-value of test no 48                 :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.44
 p-value of test no 49                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   37.23
 p-value of test no 50                 :    0.96
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   49.29
 p-value of test no 51                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.77
 p-value of test no 52                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.40
 p-value of test no 53                 :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  228.56
 p-value of test no 54                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  448.40
 p-value of test no 55                 :    0.31
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1396.73
 p-value of test no 56                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6866.93
 p-value of test no 57                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.47
 p-value of test no 58                 :    0.08
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 59                 :    0.61
 
 Anderson-Darling statistic = A2       :    1.69
 p-value of test no 60                 :    0.14
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   25.42
 p-value of test no 61                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 62                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 63                 :    0.93
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 64                 :    0.48
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   47.72
 p-value of test no 65                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    1.60
 p-value of test no 66                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  119.18
 p-value of test no 67                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5096.88
 p-value of test no 68                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46029
 p-value of test no 70                 :    0.24
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870029
   j =  1                              :        399907948
   j =  2                              :            46017
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:34.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46169
 p-value of test no 71                 :    0.09
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870169
   j =  1                              :        399907666
   j =  2                              :            46161
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 72                 :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    :   0.056
 p-value of test no 73                 :    0.75
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 74                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :   0.024
 p-value of test no 77                 :    0.94
 
 Anderson-Darling statistic = A2       :    1.26
 p-value of test no 78                 :    0.25
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 79                 :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 80                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.86
 p-value of test no 81                 :    0.44
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.22
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.087
 p-value of test no 83                 :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 84                 :    0.19
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 85                 :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 86                 :    0.73
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 87                 :    0.17
 
 Anderson-Darling statistic = A2       :    0.84
 p-value of test no 88                 :    0.45
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.33
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 90                 :    0.23
 
 Kolmogorov-Smirnov- statistic = D-    :   0.053
 p-value of test no 91                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.88
 p-value of test no 92                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 93                 :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 94                 :    0.77
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 95                 :    0.87
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.71
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 97                 :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :   0.063
 p-value of test no 98                 :    0.82
 
 Anderson-Darling statistic = A2       :    0.35
 p-value of test no 99                 :    0.90
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.082
 p-value of test no 100                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :   0.088
 p-value of test no 101                :    0.51
 
 Anderson-Darling statistic = A2       :    0.54
 p-value of test no 102                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 103                :    0.43
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 104                :    0.21
 
 Anderson-Darling statistic = A2       :    1.07
 p-value of test no 105                :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.047
 p-value of test no 106                :    0.89
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 107                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 108                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
 p-value of test no 109                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 3.83e-5
 p-value of test no 110                :    0.94
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 111                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
 p-value of test no 112                :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
 p-value of test no 113                :    0.44
 
 Anderson-Darling statistic = A2       :    0.41
 p-value of test no 114                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 115                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.77
 p-value of test no 116                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.13
 p-value of test no 117                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.71
 p-value of test no 118                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.76
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.77
 p-value of test no 120                :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   65.97
 p-value of test no 121                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   29.42
 p-value of test no 122                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   48.34
 p-value of test no 123                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.16
 p-value of test no 124                :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   22.20
 p-value of test no 125                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 126                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 127                :    0.03
 
 Anderson-Darling statistic = A2       :    2.10
 p-value of test no 128                :    0.08
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   53.53
 p-value of test no 129                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 130                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 131                :    0.42
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 132                :    0.79
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   43.09
 p-value of test no 133                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    5.81
 p-value of test no 134                :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    6.29
 p-value of test no 135                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 136                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    7.13
 p-value of test no 137                :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.036
 p-value of test no 138                :    0.95
 
 Kolmogorov-Smirnov- statistic = D-    :    0.40
 p-value of test no 139                :    0.03
 
 Anderson-Darling statistic = A2       :    2.18
 p-value of test no 140                :    0.07
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  157.76
 p-value of test no 141                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 142                :    0.46
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.17
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 144                :    0.52
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17469.63
 p-value of test no 145                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   58.85
 p-value of test no 146                :  9.5e-3
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.24
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   27.15
 p-value of test no 148                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.58
 p-value of test no 149                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :    8.52
 p-value of test no 150                :    0.95
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   32.16
 p-value of test no 151                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.79
 p-value of test no 152                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.46
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   31.65
 p-value of test no 154                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.99
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  161.36
 p-value of test no 156                :    0.18
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  152.79
 p-value of test no 157                :    0.33
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  518.31
 p-value of test no 158                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  136.04
 p-value of test no 159                :    0.48
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   71.85
 p-value of test no 160                :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.31
 p-value of test no 161                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  186.18
 p-value of test no 162                :    0.01
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  539.74
 p-value of test no 163                :    0.11
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  129.88
 p-value of test no 164                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   63.11
 p-value of test no 165                :    0.81
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  411.12
 p-value of test no 166                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  395.00
 p-value of test no 167                :    0.34
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4940.15
 p-value of test no 168                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  349.28
 p-value of test no 169                :    0.85
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  194.54
 p-value of test no 170                :    0.60
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  381.37
 p-value of test no 171                :    0.53
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  391.52
 p-value of test no 172                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5097.23
 p-value of test no 173                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  379.34
 p-value of test no 174                :    0.47
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  184.16
 p-value of test no 175                :    0.78
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.73
 p-value of test no 176                :    0.81
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.81
 p-value of test no 177                :    0.79
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.05
 p-value of test no 178                :    0.52
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.60
 p-value of test no 179                :    0.73
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 180                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 181                :    0.73
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 182                :    0.74
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.43
 p-value of test no 183                :    0.67
 
 Sample variance                       :    0.72
 p-value of test no 184                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 185                :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 186                :    0.43
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 187                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.016
 p-value of test no 188                :    0.51
 
 Sample variance                       :    0.48
 p-value of test no 189                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
 p-value of test no 190                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :   0.010
 p-value of test no 191                :    0.41
 
 Anderson-Darling statistic = A2       :    0.43
 p-value of test no 192                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 193                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
 p-value of test no 194                :    0.58
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 195                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    3.62
 p-value of test no 196                :    0.89
 
 -----------------------------------------------
 Global longest run of 1               :   34.00
 p-value of test no 197                :    0.25
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:15.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.13
 p-value of test no 198                :    0.63
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 200                :    0.52
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 201                :    0.74
 
 Anderson-Darling statistic = A2       :    0.25
 p-value of test no 202                :    0.97
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  201.79
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.052
 p-value of test no 205                :    0.92
 
 Anderson-Darling statistic = A2       :    0.76
 p-value of test no 206                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  180.54
 p-value of test no 207                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
 p-value of test no 208                :    0.9909
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 209                :    0.21
 
 Anderson-Darling statistic = A2       :    1.39
 p-value of test no 210                :    0.21
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10242.03
 p-value of test no 211                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.26
 p-value of test no 212                :    0.22
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.66
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 214                :    0.56
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10025.92
 p-value of test no 215                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.33
 p-value of test no 216                :    0.63
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.17
 p-value of test no 217                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.43
 p-value of test no 218                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:03:27.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 219                :    0.48
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 220                :    0.25
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 221                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4894.98
 p-value of test no 222                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.095
 p-value of test no 223                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 224                :    0.10
 
 Anderson-Darling statistic = A2       :    1.99
 p-value of test no 225                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 5028.12
 p-value of test no 226                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4111.75
 p-value of test no 227                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4234.84
 p-value of test no 228                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11852.59
 p-value of test no 229                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11681.11
 p-value of test no 230                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   48.00
 p-value of test no 231                :    0.70
 
 
 -----------------------------------------------
 Total number of bits:  8000117097
 
 Normal statistic for number of bits   :    0.93
 p-value of test no 232                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.29
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.87
 p-value of test no 233                :    0.44
 
 
 -----------------------------------------------
 Total number of bits:  7999948833
 
 Normal statistic for number of bits   :   -0.40
 p-value of test no 234                :    0.66
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 235                :  5.0e-3
 
 Kolmogorov-Smirnov- statistic = D-    :   0.016
 p-value of test no 236                :    0.98
 
 Anderson-Darling statistic = A2       :    4.35
 p-value of test no 237                :  6.2e-3
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -2.78
 p-value of test no 238                :    0.9973
 
 Sample variance                       :    0.52
 p-value of test no 239                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 240                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 241                :    0.13
 
 Anderson-Darling statistic = A2       :    0.70
 p-value of test no 242                :    0.56
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.13
 p-value of test no 243                :    0.45
 
 Sample variance                       :    0.44
 p-value of test no 244                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 245                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 246                :    0.72
 
 Anderson-Darling statistic = A2       :    0.16
 p-value of test no 247                :    0.9980
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 248                :    0.54
 
 Sample variance                       :    1.09
 p-value of test no 249                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.097
 p-value of test no 250                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.38
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 252                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.32
 p-value of test no 253                :    0.37
 
 Sample variance                       :    1.08
 p-value of test no 254                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.72
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:41.45
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35996
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :  6.9e-4    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.51
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1430
 p-value of test no 3                  :    0.04
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334550
   j =  1                              :        599997140
   j =  2                              :             1430
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1335
 p-value of test no 4                  :    0.78
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334455
   j =  1                              :        599997330
   j =  2                              :             1335
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:12.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1409
 p-value of test no 5                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334529
   j =  1                              :        599997182
   j =  2                              :             1409
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1334
 p-value of test no 6                  :    0.79
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334454
   j =  1                              :        599997332
   j =  2                              :             1334
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1366
 p-value of test no 7                  :    0.48
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334486
   j =  1                              :        599997268
   j =  2                              :             1366
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:43.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1408
 p-value of test no 8                  :    0.12
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334528
   j =  1                              :        599997184
   j =  2                              :             1408
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:03.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1289
 p-value of test no 9                  :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334409
   j =  1                              :        599997422
   j =  2                              :             1289
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1357
 p-value of test no 10                 :    0.57
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334477
   j =  1                              :        599997286
   j =  2                              :             1357
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 11                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1454
 p-value of test no 12                 :  8.3e-3
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334574
   j =  1                              :        599997092
   j =  2                              :             1454
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5412
 p-value of test no 13                 :    0.55
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4376
 p-value of test no 14                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7395
 p-value of test no 15                 :    0.19
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4291
 p-value of test no 16                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4293
 p-value of test no 17                 :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7507
 p-value of test no 18                 :    0.01
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7274
 p-value of test no 19                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7461
 p-value of test no 20                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7149
 p-value of test no 21                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.80
 p-value of test no 22                 :    0.48
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.86
 p-value of test no 23                 :    0.11
 
 Test on the Nm values of W_{n,i}(mNP1):    0.92
 p-value of test no 24                 :    0.40
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     854
 p-value of test no 25                 :    0.94
 
 Stat. AD (mNP2)                       :    1.34
 p-value of test no 26                 :    0.22
 
 Stat. AD after spacings (mNP2-S)      :    3.74
 p-value of test no 27                 :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:43.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.49
 p-value of test no 28                 :    0.75
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.69
 p-value of test no 29                 :    0.14
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     606
 p-value of test no 31                 :    0.41
 
 Stat. AD (mNP2)                       :    0.64
 p-value of test no 32                 :    0.61
 
 Stat. AD after spacings (mNP2-S)      :    1.17
 p-value of test no 33                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.37
 p-value of test no 34                 :    0.87
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.57
 p-value of test no 35                 :    0.67
 
 Test on the Nm values of W_{n,i}(mNP1):    0.64
 p-value of test no 36                 :    0.61
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     296
 p-value of test no 37                 :    0.58
 
 Stat. AD (mNP2)                       :    0.37
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    0.64
 p-value of test no 39                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:02:06.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.42
 p-value of test no 40                 :    0.20
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.95
 p-value of test no 41                 :    0.38
 
 Test on the Nm values of W_{n,i}(mNP1):    0.79
 p-value of test no 42                 :    0.49
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     142
 p-value of test no 43                 :    0.73
 
 Stat. AD (mNP2)                       :    0.68
 p-value of test no 44                 :    0.58
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 45                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.39
 p-value of test no 46                 :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    4.53
 p-value of test no 47                 :    0.72
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.45
 p-value of test no 48                 :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.35
 p-value of test no 49                 :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.30
 p-value of test no 50                 :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   44.67
 p-value of test no 51                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   41.81
 p-value of test no 52                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   58.94
 p-value of test no 53                 :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  243.22
 p-value of test no 54                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  434.26
 p-value of test no 55                 :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1456.78
 p-value of test no 56                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:01:04.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7007.97
 p-value of test no 57                 :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.48
 p-value of test no 58                 :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 59                 :    0.70
 
 Anderson-Darling statistic = A2       :    1.64
 p-value of test no 60                 :    0.15
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   19.15
 p-value of test no 61                 :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 62                 :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :   0.091
 p-value of test no 63                 :    0.80
 
 Anderson-Darling statistic = A2       :    1.81
 p-value of test no 64                 :    0.12
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.86
 p-value of test no 65                 :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   16.78
 p-value of test no 66                 :  4.9e-3
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.59
 p-value of test no 67                 :    0.82
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4991.53
 p-value of test no 68                 :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45884
 p-value of test no 70                 :    0.49
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869884
   j =  1                              :        399908236
   j =  2                              :            45876
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:33.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45824
 p-value of test no 71                 :    0.60
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869824
   j =  1                              :        399908360
   j =  2                              :            45808
   j =  3                              :                8
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:37.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 72                 :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.012
 p-value of test no 73                 :    0.98
 
 Anderson-Darling statistic = A2       :    2.88
 p-value of test no 74                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 3.99e+6
 p-value of test no 75                 :    0.9905
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 76                 :    0.15
 
 Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
 p-value of test no 77                 :    0.9934
 
 Anderson-Darling statistic = A2       :    1.75
 p-value of test no 78                 :    0.13
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 79                 :    0.49
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 80                 :    0.72
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 81                 :    0.90
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.59
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 83                 :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :   0.045
 p-value of test no 84                 :    0.86
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 85                 :    0.65
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 86                 :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
 p-value of test no 87                 :    0.9954
 
 Anderson-Darling statistic = A2       :    2.48
 p-value of test no 88                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.99
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 90                 :    0.59
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 91                 :    0.35
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 92                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 93                 :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :   0.080
 p-value of test no 94                 :    0.74
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 95                 :    0.73
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.69
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.088
 p-value of test no 97                 :    0.69
 
 Kolmogorov-Smirnov- statistic = D-    :    0.27
 p-value of test no 98                 :    0.04
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 99                 :    0.34
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:26.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 100                :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 101                :    0.12
 
 Anderson-Darling statistic = A2       :    1.72
 p-value of test no 102                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:34.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 103                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.068
 p-value of test no 104                :    0.80
 
 Anderson-Darling statistic = A2       :    1.74
 p-value of test no 105                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 106                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :   0.073
 p-value of test no 107                :    0.77
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 108                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
 p-value of test no 109                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
 p-value of test no 110                :    0.70
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 111                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
 p-value of test no 112                :    0.62
 
 Kolmogorov-Smirnov- statistic = D-    : 7.97e-5
 p-value of test no 113                :    0.78
 
 Anderson-Darling statistic = A2       :    0.19
 p-value of test no 114                :    0.9920
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.65
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.74
 p-value of test no 116                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:09.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.38
 p-value of test no 117                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.31
 p-value of test no 118                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   83.97
 p-value of test no 119                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   61.75
 p-value of test no 120                :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   62.17
 p-value of test no 121                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.64
 p-value of test no 122                :    0.90
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   38.38
 p-value of test no 123                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.79
 p-value of test no 124                :    0.83
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   36.52
 p-value of test no 125                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 126                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 127                :    0.72
 
 Anderson-Darling statistic = A2       :    0.90
 p-value of test no 128                :    0.41
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   34.58
 p-value of test no 129                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 130                :    0.76
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 131                :    0.07
 
 Anderson-Darling statistic = A2       :    1.13
 p-value of test no 132                :    0.29
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   44.65
 p-value of test no 133                :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    0.94
 p-value of test no 134                :    0.82
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 135                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.03
 p-value of test no 136                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:11.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.40
 p-value of test no 137                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 138                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 139                :    0.65
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 140                :    0.83
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  125.27
 p-value of test no 141                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.42
 p-value of test no 142                :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 143                :    0.64
 
 Anderson-Darling statistic = A2       :    2.59
 p-value of test no 144                :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17114.68
 p-value of test no 145                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   36.90
 p-value of test no 146                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   30.75
 p-value of test no 147                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   28.02
 p-value of test no 148                :    0.31
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   27.32
 p-value of test no 149                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   18.36
 p-value of test no 150                :    0.37
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.83
 p-value of test no 151                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   27.38
 p-value of test no 152                :    0.82
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   20.44
 p-value of test no 153                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   22.02
 p-value of test no 154                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.99
 p-value of test no 155                :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  149.67
 p-value of test no 156                :    0.40
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  159.89
 p-value of test no 157                :    0.20
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  522.23
 p-value of test no 158                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  140.03
 p-value of test no 159                :    0.39
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   97.44
 p-value of test no 160                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  182.29
 p-value of test no 161                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  145.80
 p-value of test no 162                :    0.49
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  564.35
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :   93.11
 p-value of test no 164                :    0.9981
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   72.06
 p-value of test no 165                :    0.54
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  369.06
 p-value of test no 166                :    0.70
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  389.27
 p-value of test no 167                :    0.42
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5056.20
 p-value of test no 168                :    0.29
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  390.30
 p-value of test no 169                :    0.32
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  236.56
 p-value of test no 170                :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  371.96
 p-value of test no 171                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  426.83
 p-value of test no 172                :    0.06
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4933.76
 p-value of test no 173                :    0.74
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.36
 p-value of test no 174                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  243.09
 p-value of test no 175                :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    7.59
 p-value of test no 176                :    0.82
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -1.70
 p-value of test no 177                :    0.96
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   11.21
 p-value of test no 178                :    0.51
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.23
 p-value of test no 179                :    0.41
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.30
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 180                :    0.37
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 181                :    0.51
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 182                :    0.59
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.34
 p-value of test no 183                :    0.37
 
 Sample variance                       :    1.69
 p-value of test no 184                :    0.09
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
 p-value of test no 185                :    0.9942
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 186                :    0.22
 
 Anderson-Darling statistic = A2       :    1.42
 p-value of test no 187                :    0.20
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.72
 p-value of test no 188                :    0.04
 
 Sample variance                       :    0.96
 p-value of test no 189                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.010
 p-value of test no 190                :    0.41
 
 Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
 p-value of test no 191                :    0.76
 
 Anderson-Darling statistic = A2       :    0.60
 p-value of test no 192                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
 p-value of test no 193                :    0.54
 
 Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
 p-value of test no 194                :    0.89
 
 Anderson-Darling statistic = A2       :    0.68
 p-value of test no 195                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   18.34
 p-value of test no 196                :    0.02
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   22.01
 p-value of test no 198                :  4.9e-3
 
 -----------------------------------------------
 Global longest run of 1               :   30.00
 p-value of test no 199                :    0.90
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:18.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 200                :    0.57
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 201                :    0.06
 
 Anderson-Darling statistic = A2       :    1.22
 p-value of test no 202                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  209.87
 p-value of test no 203                :    0.30
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 204                :    0.25
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 205                :    0.45
 
 Anderson-Darling statistic = A2       :    0.83
 p-value of test no 206                :    0.46
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  187.20
 p-value of test no 207                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 208                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.50
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 210                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10020.46
 p-value of test no 211                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.079
 p-value of test no 212                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 213                :    0.05
 
 Anderson-Darling statistic = A2       :    1.90
 p-value of test no 214                :    0.11
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10220.07
 p-value of test no 215                :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:43.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.88
 p-value of test no 216                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 217                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.62
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.61
 p-value of test no 218                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 219                :    0.78
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 220                :    0.61
 
 Anderson-Darling statistic = A2       :    0.44
 p-value of test no 221                :    0.81
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4895.64
 p-value of test no 222                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 223                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 224                :    0.64
 
 Anderson-Darling statistic = A2       :    0.53
 p-value of test no 225                :    0.72
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4851.06
 p-value of test no 226                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:24.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4120.93
 p-value of test no 227                :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4057.82
 p-value of test no 228                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11459.44
 p-value of test no 229                :    0.9917
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11784.13
 p-value of test no 230                :    0.60
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   61.32
 p-value of test no 231                :    0.23
 
 
 -----------------------------------------------
 Total number of bits:  8000010315
 
 Normal statistic for number of bits   :   0.082
 p-value of test no 232                :    0.47
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000001
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   64.09
 p-value of test no 233                :    0.16
 
 
 -----------------------------------------------
 Total number of bits:  8000003397
 
 Normal statistic for number of bits   :   0.027
 p-value of test no 234                :    0.49
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 235                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 236                :    0.25
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 237                :    0.66
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.11
 p-value of test no 238                :    0.46
 
 Sample variance                       :    1.23
 p-value of test no 239                :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 240                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 241                :    0.61
 
 Anderson-Darling statistic = A2       :    1.79
 p-value of test no 242                :    0.12
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -1.29
 p-value of test no 243                :    0.90
 
 Sample variance                       :    1.52
 p-value of test no 244                :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.054
 p-value of test no 245                :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 246                :    0.47
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 247                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.87
 p-value of test no 248                :    0.19
 
 Sample variance                       :    0.96
 p-value of test no 249                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 250                :    0.09
 
 Kolmogorov-Smirnov- statistic = D-    :    0.21
 p-value of test no 251                :    0.36
 
 Anderson-Darling statistic = A2       :    2.15
 p-value of test no 252                :    0.08
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.56
 p-value of test no 253                :    0.71
 
 Sample variance                       :    2.31
 p-value of test no 254                :    0.01
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.55
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:39:31.23
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
   1  SerialOver, r = 0               6.9e-4
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35997
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1378
 p-value of test no 3                  :    0.36
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334498
   j =  1                              :        599997244
   j =  2                              :             1378
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1345
 p-value of test no 4                  :    0.69
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334465
   j =  1                              :        599997310
   j =  2                              :             1345
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1392
 p-value of test no 5                  :    0.23
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334512
   j =  1                              :        599997216
   j =  2                              :             1392
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:38.66
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1377
 p-value of test no 6                  :    0.37
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334497
   j =  1                              :        599997246
   j =  2                              :             1377
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:05.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1344
 p-value of test no 7                  :    0.70
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334464
   j =  1                              :        599997312
   j =  2                              :             1344
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1368
 p-value of test no 8                  :    0.46
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334488
   j =  1                              :        599997264
   j =  2                              :             1368
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1385
 p-value of test no 9                  :    0.29
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334505
   j =  1                              :        599997230
   j =  2                              :             1385
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:37.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1394
 p-value of test no 10                 :    0.21
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334514
   j =  1                              :        599997212
   j =  2                              :             1394
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:56.01
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1288
 p-value of test no 11                 :    0.98
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334408
   j =  1                              :        599997424
   j =  2                              :             1288
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1437
 p-value of test no 12                 :    0.03
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334557
   j =  1                              :        599997126
   j =  2                              :             1437
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5382
 p-value of test no 13                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4444
 p-value of test no 14                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7139
 p-value of test no 15                 :    0.98
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4456
 p-value of test no 16                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:38.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4351
 p-value of test no 17                 :    0.42
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7046
 p-value of test no 18                 :    0.9993    *****
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7340
 p-value of test no 19                 :    0.40
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7261
 p-value of test no 20                 :    0.75
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:03.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7327
 p-value of test no 21                 :    0.46
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:07.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.75
 p-value of test no 22                 :    0.52
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.72
 p-value of test no 23                 :    0.13
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 24                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     891
 p-value of test no 25                 :    0.61
 
 Stat. AD (mNP2)                       :    0.63
 p-value of test no 26                 :    0.62
 
 Stat. AD after spacings (mNP2-S)      :    2.45
 p-value of test no 27                 :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:42.94
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.91
 p-value of test no 28                 :    0.41
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.27
 p-value of test no 29                 :    0.96
 
 Test on the Nm values of W_{n,i}(mNP1):    1.21
 p-value of test no 30                 :    0.26
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     588
 p-value of test no 31                 :    0.68
 
 Stat. AD (mNP2)                       :    0.41
 p-value of test no 32                 :    0.84
 
 Stat. AD after spacings (mNP2-S)      :    1.83
 p-value of test no 33                 :    0.11
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.26
 p-value of test no 34                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.48
 p-value of test no 35                 :    0.76
 
 Test on the Nm values of W_{n,i}(mNP1):    3.54
 p-value of test no 36                 :    0.01
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     343
 p-value of test no 37                 :  8.0e-3
 
 Stat. AD (mNP2)                       :    0.77
 p-value of test no 38                 :    0.50
 
 Stat. AD after spacings (mNP2-S)      :    1.31
 p-value of test no 39                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.29
 p-value of test no 40                 :    0.94
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.39
 p-value of test no 41                 :    0.21
 
 Test on the Nm values of W_{n,i}(mNP1):    0.73
 p-value of test no 42                 :    0.54
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     147
 p-value of test no 43                 :    0.58
 
 Stat. AD (mNP2)                       :    2.57
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.26
 p-value of test no 45                 :    0.25
 
 -----------------------------------------------
 CPU time used                    :  00:02:31.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    9.32
 p-value of test no 46                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.12
 p-value of test no 47                 :    0.53
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   23.16
 p-value of test no 48                 :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   14.98
 p-value of test no 49                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.44
 p-value of test no 50                 :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:47.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   61.10
 p-value of test no 51                 :    0.24
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   57.62
 p-value of test no 52                 :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   60.04
 p-value of test no 53                 :    0.27
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  260.22
 p-value of test no 54                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  445.02
 p-value of test no 55                 :    0.35
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1514.27
 p-value of test no 56                 :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7268.31
 p-value of test no 57                 :    0.03
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.49
 p-value of test no 58                 :    0.06
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 59                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.00
 p-value of test no 60                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   17.52
 p-value of test no 61                 :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:49.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 63                 :    0.76
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 64                 :    0.53
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.22
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:10.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    4.59
 p-value of test no 66                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  113.11
 p-value of test no 67                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4937.29
 p-value of test no 68                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.04
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46200
 p-value of test no 70                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870200
   j =  1                              :        399907603
   j =  2                              :            46194
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46314
 p-value of test no 71                 :    0.02
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870314
   j =  1                              :        399907375
   j =  2                              :            46308
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 72                 :    0.98
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 73                 :    0.16
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 74                 :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.05
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 76                 :    0.19
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 77                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.80
 p-value of test no 78                 :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.050
 p-value of test no 79                 :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 80                 :    0.11
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 81                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.17
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.029
 p-value of test no 83                 :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.26
 p-value of test no 84                 :    0.01
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 85                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:45.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.34
 p-value of test no 86                 :  6.6e-3
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 87                 :    0.56
 
 Anderson-Darling statistic = A2       :    2.06
 p-value of test no 88                 :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.87
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 90                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.039
 p-value of test no 91                 :    0.92
 
 Anderson-Darling statistic = A2       :    0.69
 p-value of test no 92                 :    0.56
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.053
 p-value of test no 93                 :    0.86
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 94                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.29
 p-value of test no 95                 :    0.24
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.10
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 97                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 98                 :    0.08
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 99                 :    0.33
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:25.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.100
 p-value of test no 100                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 101                :    0.42
 
 Anderson-Darling statistic = A2       :    1.03
 p-value of test no 102                :    0.34
 
 -----------------------------------------------
 CPU time used                    :  00:01:33.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 103                :    0.21
 
 Kolmogorov-Smirnov- statistic = D-    :   0.085
 p-value of test no 104                :    0.71
 
 Anderson-Darling statistic = A2       :    0.45
 p-value of test no 105                :    0.80
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 106                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.011
 p-value of test no 107                :    0.99
 
 Anderson-Darling statistic = A2       :    0.96
 p-value of test no 108                :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
 p-value of test no 109                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
 p-value of test no 110                :    0.24
 
 Anderson-Darling statistic = A2       :    0.98
 p-value of test no 111                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
 p-value of test no 112                :    0.42
 
 Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
 p-value of test no 113                :    0.67
 
 Anderson-Darling statistic = A2       :    0.29
 p-value of test no 114                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.16
 p-value of test no 115                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.57
 p-value of test no 116                :    0.9949
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.18
 p-value of test no 117                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.12
 p-value of test no 118                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   68.52
 p-value of test no 119                :    0.43
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   73.91
 p-value of test no 120                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   85.07
 p-value of test no 121                :    0.07
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   35.30
 p-value of test no 122                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:22.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   28.44
 p-value of test no 123                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   46.48
 p-value of test no 124                :    0.14
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   28.06
 p-value of test no 125                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 126                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 127                :    0.17
 
 Anderson-Darling statistic = A2       :    1.35
 p-value of test no 128                :    0.22
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   41.24
 p-value of test no 129                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 130                :    0.70
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 131                :    0.25
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.08
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.20
 p-value of test no 134                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.21
 p-value of test no 135                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.23
 p-value of test no 136                :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    0.27
 p-value of test no 137                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 138                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 139                :    0.61
 
 Anderson-Darling statistic = A2       :    0.24
 p-value of test no 140                :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  124.88
 p-value of test no 141                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:00:20.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.046
 p-value of test no 142                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 143                :    0.16
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 144                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17586.69
 p-value of test no 145                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   33.27
 p-value of test no 146                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   36.16
 p-value of test no 147                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   18.17
 p-value of test no 148                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   29.24
 p-value of test no 149                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   15.92
 p-value of test no 150                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   37.19
 p-value of test no 151                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   40.85
 p-value of test no 152                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   19.50
 p-value of test no 153                :    0.77
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   17.41
 p-value of test no 154                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.90
 p-value of test no 155                :    0.74
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.57
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  143.28
 p-value of test no 156                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  130.64
 p-value of test no 157                :    0.81
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  511.74
 p-value of test no 158                :    0.35
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  115.69
 p-value of test no 159                :    0.90
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   58.09
 p-value of test no 160                :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  127.06
 p-value of test no 161                :    0.87
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  157.55
 p-value of test no 162                :    0.24
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  565.67
 p-value of test no 163                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  138.98
 p-value of test no 164                :    0.41
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.27
 p-value of test no 165                :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  392.15
 p-value of test no 166                :    0.38
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  401.52
 p-value of test no 167                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4854.52
 p-value of test no 168                :    0.93
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  393.24
 p-value of test no 169                :    0.28
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  185.78
 p-value of test no 170                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  325.78
 p-value of test no 171                :    0.99
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  311.85
 p-value of test no 172                :    0.9971
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4959.59
 p-value of test no 173                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  398.36
 p-value of test no 174                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  197.67
 p-value of test no 175                :    0.53
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.38
 p-value of test no 176                :    0.34
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.97
 p-value of test no 177                :    0.17
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   13.20
 p-value of test no 178                :    0.35
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    1.70
 p-value of test no 179                :    0.04
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 180                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.35
 p-value of test no 181                :    0.07
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 182                :    0.35
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.78
 p-value of test no 183                :    0.22
 
 Sample variance                       :    0.88
 p-value of test no 184                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 185                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 186                :    0.55
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 187                :    0.33
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.70
 p-value of test no 188                :    0.76
 
 Sample variance                       :    0.29
 p-value of test no 189                :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 190                :    0.35
 
 Kolmogorov-Smirnov- statistic = D-    : 3.14e-3
 p-value of test no 191                :    0.92
 
 Anderson-Darling statistic = A2       :    0.77
 p-value of test no 192                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
 p-value of test no 193                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
 p-value of test no 194                :    0.86
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 195                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   10.99
 p-value of test no 196                :    0.20
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 197                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    6.69
 p-value of test no 198                :    0.57
 
 -----------------------------------------------
 Global longest run of 1               :   29.00
 p-value of test no 199                :    0.9905
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 200                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.058
 p-value of test no 201                :    0.90
 
 Anderson-Darling statistic = A2       :    1.55
 p-value of test no 202                :    0.16
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  172.27
 p-value of test no 203                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:55.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 204                :    0.61
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 205                :    0.68
 
 Anderson-Darling statistic = A2       :    0.27
 p-value of test no 206                :    0.96
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  194.02
 p-value of test no 207                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 208                :    0.17
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 209                :    0.51
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 210                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9974.44
 p-value of test no 211                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 212                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.22
 p-value of test no 213                :    0.34
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 214                :    0.78
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10026.22
 p-value of test no 215                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.70
 p-value of test no 216                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:00:55.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -2.83
 p-value of test no 217                :    0.9977
 
 -----------------------------------------------
 CPU time used                    :  00:00:53.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.53
 p-value of test no 218                :    0.70
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 219                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.087
 p-value of test no 220                :    0.82
 
 Anderson-Darling statistic = A2       :    1.41
 p-value of test no 221                :    0.20
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4752.49
 p-value of test no 222                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.21
 p-value of test no 223                :    0.36
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 225                :    0.61
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4871.14
 p-value of test no 226                :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:01:22.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4280.68
 p-value of test no 227                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4302.18
 p-value of test no 228                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.45
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11825.73
 p-value of test no 229                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.79
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11923.26
 p-value of test no 230                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:01:07.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   56.02
 p-value of test no 231                :    0.40
 
 
 -----------------------------------------------
 Total number of bits:  7999845504
 
 Normal statistic for number of bits   :   -1.22
 p-value of test no 232                :    0.89
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   53.62
 p-value of test no 233                :    0.49
 
 
 -----------------------------------------------
 Total number of bits:  8000092194
 
 Normal statistic for number of bits   :    0.73
 p-value of test no 234                :    0.23
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.022
 p-value of test no 235                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 236                :    0.11
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.59
 p-value of test no 238                :    0.06
 
 Sample variance                       :    0.73
 p-value of test no 239                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.33
 p-value of test no 240                :    0.10
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 241                :    0.75
 
 Anderson-Darling statistic = A2       :    0.85
 p-value of test no 242                :    0.44
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.73
 p-value of test no 243                :    0.77
 
 Sample variance                       :    0.58
 p-value of test no 244                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 245                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 246                :    0.44
 
 Anderson-Darling statistic = A2       :    1.06
 p-value of test no 247                :    0.32
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.39
 p-value of test no 248                :    0.35
 
 Sample variance                       :    2.22
 p-value of test no 249                :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 250                :    0.44
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 251                :    0.60
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 252                :    0.92
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.12
 p-value of test no 253                :    0.45
 
 Sample variance                       :    0.81
 p-value of test no 254                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.02
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:38:56.47
  The following tests gave p-values outside [0.001, 0.9990]:
  (eps  means a value < 1.0e-300):
  (eps1 means a value < 1.0e-15):
 
        Test                          p-value
  ----------------------------------------------
  18  BirthdaySpacings, t = 8         0.9993 
  ----------------------------------------------
  All other tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35998
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.80
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.95
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.32
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1350
 p-value of test no 3                  :    0.64
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334470
   j =  1                              :        599997300
   j =  2                              :             1350
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:53.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1305
 p-value of test no 4                  :    0.94
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334425
   j =  1                              :        599997390
   j =  2                              :             1305
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1318
 p-value of test no 5                  :    0.89
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334438
   j =  1                              :        599997364
   j =  2                              :             1318
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1358
 p-value of test no 6                  :    0.56
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334478
   j =  1                              :        599997284
   j =  2                              :             1358
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:00.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1353
 p-value of test no 7                  :    0.61
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334473
   j =  1                              :        599997294
   j =  2                              :             1353
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1382
 p-value of test no 8                  :    0.32
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334502
   j =  1                              :        599997236
   j =  2                              :             1382
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:55.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 9                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:30.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1316
 p-value of test no 10                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334436
   j =  1                              :        599997368
   j =  2                              :             1316
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1393
 p-value of test no 11                 :    0.22
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334513
   j =  1                              :        599997214
   j =  2                              :             1393
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:23.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1317
 p-value of test no 12                 :    0.90
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334437
   j =  1                              :        599997366
   j =  2                              :             1317
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5387
 p-value of test no 13                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4409
 p-value of test no 14                 :    0.14
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:29.92
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7383
 p-value of test no 15                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4345
 p-value of test no 16                 :    0.45
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.34
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4301
 p-value of test no 17                 :    0.70
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7225
 p-value of test no 18                 :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7364
 p-value of test no 19                 :    0.30
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:34.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7257
 p-value of test no 20                 :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:04.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7300
 p-value of test no 21                 :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.85
 p-value of test no 22                 :    0.11
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.34
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    4.30
 p-value of test no 24                 :  6.2e-3
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     967
 p-value of test no 25                 :    0.01
 
 Stat. AD (mNP2)                       :    0.95
 p-value of test no 26                 :    0.38
 
 Stat. AD after spacings (mNP2-S)      :    1.30
 p-value of test no 27                 :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:41.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.48
 p-value of test no 28                 :    0.76
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.46
 p-value of test no 30                 :    0.79
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     593
 p-value of test no 31                 :    0.60
 
 Stat. AD (mNP2)                       :    1.86
 p-value of test no 32                 :    0.11
 
 Stat. AD after spacings (mNP2-S)      :    0.44
 p-value of test no 33                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    1.29
 p-value of test no 34                 :    0.23
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 35                 :    0.65
 
 Test on the Nm values of W_{n,i}(mNP1):    0.62
 p-value of test no 36                 :    0.63
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     320
 p-value of test no 37                 :    0.13
 
 Stat. AD (mNP2)                       :    0.38
 p-value of test no 38                 :    0.87
 
 Stat. AD after spacings (mNP2-S)      :    1.62
 p-value of test no 39                 :    0.15
 
 -----------------------------------------------
 CPU time used                    :  00:02:05.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    3.75
 p-value of test no 40                 :    0.01
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 41                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.82
 p-value of test no 42                 :    0.47
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     141
 p-value of test no 43                 :    0.75
 
 Stat. AD (mNP2)                       :    1.17
 p-value of test no 44                 :    0.28
 
 Stat. AD after spacings (mNP2-S)      :    0.59
 p-value of test no 45                 :    0.66
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.65
 p-value of test no 46                 :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    7.09
 p-value of test no 47                 :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:50.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   33.00
 p-value of test no 48                 :    0.02
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   25.23
 p-value of test no 49                 :    0.12
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.48
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   48.82
 p-value of test no 50                 :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   45.84
 p-value of test no 51                 :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.91
 p-value of test no 52                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   42.15
 p-value of test no 53                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  241.33
 p-value of test no 54                 :    0.32
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  398.15
 p-value of test no 55                 :    0.89
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1532.49
 p-value of test no 56                 :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 6907.90
 p-value of test no 57                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:57.18
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.19
 p-value of test no 58                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :    0.41
 p-value of test no 59                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.01
 p-value of test no 60                 :    0.35
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   34.09
 p-value of test no 61                 :    0.28
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 62                 :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 63                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.79
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   51.55
 p-value of test no 65                 :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :    2.05
 p-value of test no 66                 :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  122.53
 p-value of test no 67                 :    0.39
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 5009.28
 p-value of test no 68                 :    0.61
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.62e+6
 p-value of test no 69                 :    0.9986
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:46.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45684
 p-value of test no 70                 :    0.82
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869684
   j =  1                              :        399908638
   j =  2                              :            45672
   j =  3                              :                6
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:32.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46213
 p-value of test no 71                 :    0.06
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870213
   j =  1                              :        399907578
   j =  2                              :            46205
   j =  3                              :                4
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:36.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.096
 p-value of test no 72                 :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    :   0.047
 p-value of test no 73                 :    0.81
 
 Anderson-Darling statistic = A2       :    0.66
 p-value of test no 74                 :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.66
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 76                 :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 77                 :    0.56
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 78                 :    0.66
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.035
 p-value of test no 79                 :    0.91
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 80                 :  6.1e-3
 
 Anderson-Darling statistic = A2       :    2.43
 p-value of test no 81                 :    0.05
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.04
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 83                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
 p-value of test no 84                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.19
 p-value of test no 85                 :    0.07
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.092
 p-value of test no 86                 :    0.67
 
 Kolmogorov-Smirnov- statistic = D-    :   0.072
 p-value of test no 87                 :    0.78
 
 Anderson-Darling statistic = A2       :    0.22
 p-value of test no 88                 :    0.98
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :    0.55
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 90                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
 p-value of test no 91                 :    0.99
 
 Anderson-Darling statistic = A2       :    2.90
 p-value of test no 92                 :    0.03
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.31
 p-value of test no 93                 :    0.02
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 94                 :    0.54
 
 Anderson-Darling statistic = A2       :    2.34
 p-value of test no 95                 :    0.06
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.80
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.045
 p-value of test no 97                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.12
 p-value of test no 98                 :    0.50
 
 Anderson-Darling statistic = A2       :    0.33
 p-value of test no 99                 :    0.91
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:27.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
 p-value of test no 100                :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 101                :  3.9e-4    *****
 
 Anderson-Darling statistic = A2       :    4.63
 p-value of test no 102                :  4.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.12
 p-value of test no 103                :    0.50
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 104                :    0.29
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 105                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 106                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 107                :    0.27
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 108                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
 p-value of test no 109                :    0.20
 
 Kolmogorov-Smirnov- statistic = D-    : 5.48e-5
 p-value of test no 110                :    0.89
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 111                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
 p-value of test no 112                :    0.45
 
 Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
 p-value of test no 113                :    0.56
 
 Anderson-Darling statistic = A2       :    0.51
 p-value of test no 114                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.62
 p-value of test no 115                :    0.95
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.15
 p-value of test no 116                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.63
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    1.43
 p-value of test no 117                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.12
 p-value of test no 118                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   75.66
 p-value of test no 119                :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.51
 p-value of test no 120                :    0.73
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   66.52
 p-value of test no 121                :    0.49
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   33.36
 p-value of test no 122                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:24.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   25.80
 p-value of test no 123                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   37.64
 p-value of test no 124                :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   27.53
 p-value of test no 125                :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.32
 p-value of test no 126                :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :   0.079
 p-value of test no 127                :    0.84
 
 Anderson-Darling statistic = A2       :    0.75
 p-value of test no 128                :    0.51
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   32.61
 p-value of test no 129                :    0.79
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.081
 p-value of test no 130                :    0.84
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 131                :    0.17
 
 Anderson-Darling statistic = A2       :    1.21
 p-value of test no 132                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   48.10
 p-value of test no 133                :    0.18
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.65
 p-value of test no 134                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    1.45
 p-value of test no 135                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:21.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.53
 p-value of test no 136                :    0.47
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.64
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    1.37
 p-value of test no 137                :    0.51
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.094
 p-value of test no 138                :    0.79
 
 Kolmogorov-Smirnov- statistic = D-    :    0.36
 p-value of test no 139                :    0.06
 
 Anderson-Darling statistic = A2       :    1.23
 p-value of test no 140                :    0.26
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  143.01
 p-value of test no 141                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 142                :    0.55
 
 Kolmogorov-Smirnov- statistic = D-    :    0.30
 p-value of test no 143                :    0.14
 
 Anderson-Darling statistic = A2       :    1.19
 p-value of test no 144                :    0.27
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17597.94
 p-value of test no 145                :    0.18
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   29.02
 p-value of test no 146                :    0.79
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   28.74
 p-value of test no 147                :    0.76
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   21.71
 p-value of test no 148                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   24.28
 p-value of test no 149                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   11.28
 p-value of test no 150                :    0.84
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.00
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   31.79
 p-value of test no 151                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   44.43
 p-value of test no 152                :    0.13
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   35.08
 p-value of test no 153                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.82
 p-value of test no 154                :    0.86
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   12.59
 p-value of test no 155                :    0.76
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  156.78
 p-value of test no 156                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  163.11
 p-value of test no 157                :    0.16
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  536.70
 p-value of test no 158                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  165.34
 p-value of test no 159                :    0.04
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   73.32
 p-value of test no 160                :    0.50
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  118.40
 p-value of test no 161                :    0.95
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  138.48
 p-value of test no 162                :    0.66
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  458.16
 p-value of test no 163                :    0.91
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  132.80
 p-value of test no 164                :    0.56
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   60.92
 p-value of test no 165                :    0.86
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  331.25
 p-value of test no 166                :    0.98
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  382.84
 p-value of test no 167                :    0.51
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 4986.90
 p-value of test no 168                :    0.55
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  415.81
 p-value of test no 169                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  189.93
 p-value of test no 170                :    0.68
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  388.25
 p-value of test no 171                :    0.43
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  376.19
 p-value of test no 172                :    0.60
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5188.17
 p-value of test no 173                :    0.03
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  368.85
 p-value of test no 174                :    0.62
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.34
 p-value of test no 175                :    0.29
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :    3.08
 p-value of test no 176                :    0.9950
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   0.048
 p-value of test no 177                :    0.48
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   10.46
 p-value of test no 178                :    0.58
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :    0.34
 p-value of test no 179                :    0.37
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.36
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 180                :    0.29
 
 Kolmogorov-Smirnov- statistic = D-    :    0.19
 p-value of test no 181                :    0.43
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 182                :    0.75
 
 Tests on the sum of all N observations
 Standardized normal statistic         :  -0.027
 p-value of test no 183                :    0.51
 
 Sample variance                       :    0.62
 p-value of test no 184                :    0.78
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 185                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 186                :    0.49
 
 Anderson-Darling statistic = A2       :    0.34
 p-value of test no 187                :    0.91
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.24
 p-value of test no 188                :    0.59
 
 Sample variance                       :    0.83
 p-value of test no 189                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.56
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.013
 p-value of test no 191                :    0.27
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 192                :    0.67
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.14
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
 p-value of test no 193                :    0.51
 
 Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
 p-value of test no 194                :    0.53
 
 Anderson-Darling statistic = A2       :    0.61
 p-value of test no 195                :    0.64
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    4.61
 p-value of test no 196                :    0.80
 
 -----------------------------------------------
 Global longest run of 1               :   31.00
 p-value of test no 197                :    0.69
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.09
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :   12.55
 p-value of test no 198                :    0.13
 
 -----------------------------------------------
 Global longest run of 1               :   33.00
 p-value of test no 199                :    0.44
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.98
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.16
 p-value of test no 200                :    0.56
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 201                :    0.28
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 202                :    0.75
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  202.08
 p-value of test no 203                :    0.45
 
 -----------------------------------------------
 CPU time used                    :  00:01:54.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 204                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 205                :    0.73
 
 Anderson-Darling statistic = A2       :    0.65
 p-value of test no 206                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  185.60
 p-value of test no 207                :    0.76
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.10
 p-value of test no 208                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.46
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 210                :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  :10126.30
 p-value of test no 211                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 212                :    0.66
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 213                :    0.68
 
 Anderson-Darling statistic = A2       :    0.17
 p-value of test no 214                :    0.9963
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9980.07
 p-value of test no 215                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -1.83
 p-value of test no 216                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.20
 p-value of test no 217                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.54
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.34
 p-value of test no 218                :    0.37
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.13
 p-value of test no 219                :    0.65
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 220                :    0.51
 
 Anderson-Darling statistic = A2       :    0.40
 p-value of test no 221                :    0.85
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4870.32
 p-value of test no 222                :    0.58
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 223                :    0.75
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 224                :    0.53
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 225                :    0.92
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4924.85
 p-value of test no 226                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4149.65
 p-value of test no 227                :    0.36
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.37
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4070.67
 p-value of test no 228                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11723.12
 p-value of test no 229                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.52
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11748.03
 p-value of test no 230                :    0.69
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   67.28
 p-value of test no 231                :    0.11
 
 
 -----------------------------------------------
 Total number of bits:  8000105481
 
 Normal statistic for number of bits   :    0.83
 p-value of test no 232                :    0.20
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.53
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   68.99
 p-value of test no 233                :    0.08
 
 
 -----------------------------------------------
 Total number of bits:  8000139156
 
 Normal statistic for number of bits   :    1.10
 p-value of test no 234                :    0.14
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.061
 p-value of test no 235                :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 236                :    0.08
 
 Anderson-Darling statistic = A2       :    1.43
 p-value of test no 237                :    0.19
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.39
 p-value of test no 238                :    0.08
 
 Sample variance                       :    0.81
 p-value of test no 239                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.18
 p-value of test no 240                :    0.47
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 241                :    0.60
 
 Anderson-Darling statistic = A2       :    0.42
 p-value of test no 242                :    0.83
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.26
 p-value of test no 243                :    0.60
 
 Sample variance                       :    1.38
 p-value of test no 244                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 245                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 246                :    0.79
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 247                :    0.78
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.42
 p-value of test no 248                :    0.66
 
 Sample variance                       :    0.91
 p-value of test no 249                :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 250                :    0.26
 
 Kolmogorov-Smirnov- statistic = D-    :    0.31
 p-value of test no 251                :    0.12
 
 Anderson-Darling statistic = A2       :    1.27
 p-value of test no 252                :    0.24
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   0.029
 p-value of test no 253                :    0.49
 
 Sample variance                       :    0.65
 p-value of test no 254                :    0.75
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.79
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:37:57.05
 
  All tests were passed
 
 
 
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                  Starting BigCrush
                  Version: TestU01 1.2.3
 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
                     Run no 35999
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 1                  :    0.08
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:42.21
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_SerialOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =           16777216
        Expected number per cell =   59.604645
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 16711680
 Value of the statistic                : 1.67e+7
 p-value of test no 2                  :    0.85
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1360
 p-value of test no 3                  :    0.54
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334480
   j =  1                              :        599997280
   j =  2                              :             1360
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:02:54.58
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1370
 p-value of test no 4                  :    0.44
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334490
   j =  1                              :        599997260
   j =  2                              :             1370
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:13.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1348
 p-value of test no 5                  :    0.66
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334468
   j =  1                              :        599997304
   j =  2                              :             1348
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:41.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1397
 p-value of test no 6                  :    0.19
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334517
   j =  1                              :        599997206
   j =  2                              :             1397
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:01.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1380
 p-value of test no 7                  :    0.34
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334500
   j =  1                              :        599997240
   j =  2                              :             1380
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:36.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1420
 p-value of test no 8                  :    0.07
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334540
   j =  1                              :        599997160
   j =  2                              :             1420
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:57.42
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1418
 p-value of test no 9                  :    0.08
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334538
   j =  1                              :        599997164
   j =  2                              :             1418
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:31.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1293
 p-value of test no 10                 :    0.97
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334413
   j =  1                              :        599997414
   j =  2                              :             1293
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:51.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1389
 p-value of test no 11                 :    0.25
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334509
   j =  1                              :        599997222
   j =  2                              :             1389
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:25.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test smarsa_CollisionOver calling smultin_MultinomialOver
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_MultinomialOver test:
 -----------------------------------------------
    N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellSerial
        Number of cells = d^t =      4398046511104
        Expected number per cell =  1 /  219902.33
        EColl = n^2 / (2k) =  45.47473509
        Hashing =   TRUE
 
        Collision test
 
        CollisionOver:   density = n / k =  1 /  219902.33
        Expected number of collisions = Mu =      45.47
 
 
 -----------------------------------------------
 Results of CollisionOver test:
 
 POISSON approximation                 :
 Expected number of collisions = N*Mu  :     1364.24
 Observed number of collisions         :     1371
 p-value of test no 12                 :    0.43
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :  131940795334491
   j =  1                              :        599997258
   j =  2                              :             1371
   j =  3                              :                0
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:03:39.80
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
       Number of cells = d^t = 4611686018427387904
       Lambda = Poisson mean =      54.2101
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    5421.01
 Total observed number                 :    5407
 p-value of test no 13                 :    0.57
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:32.76
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4314
 p-value of test no 14                 :    0.63
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:30.19
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7331
 p-value of test no 15                 :    0.44
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:21.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4342
 p-value of test no 16                 :    0.47
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
       Number of cells = d^t = 9223372036854775808
       Lambda = Poisson mean =     216.8404
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    4336.81
 Total observed number                 :    4386
 p-value of test no 17                 :    0.23
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:39.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7321
 p-value of test no 18                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7368
 p-value of test no 19                 :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:35.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7320
 p-value of test no 20                 :    0.49
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:06.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_BirthdaySpacings test:
 -----------------------------------------------
    N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
       Number of cells = d^t = 18446744073709551616
       Lambda = Poisson mean =     365.9182
 
 
 ----------------------------------------------------
 Total expected number = N*Lambda      :    7318.36
 Total observed number                 :    7450
 p-value of test no 21                 :    0.06
 
 
 -----------------------------------------------
 CPU time used                    :  00:03:08.59
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.55
 p-value of test no 22                 :    0.69
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.35
 p-value of test no 23                 :    0.90
 
 Test on the Nm values of W_{n,i}(mNP1):    0.42
 p-value of test no 24                 :    0.83
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     900
 Number of jumps of Y                  :     906
 p-value of test no 25                 :    0.43
 
 Stat. AD (mNP2)                       :    0.75
 p-value of test no 26                 :    0.52
 
 Stat. AD after spacings (mNP2-S)      :    0.71
 p-value of test no 27                 :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:40.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.24
 p-value of test no 28                 :    0.97
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.59
 p-value of test no 29                 :    0.66
 
 Test on the Nm values of W_{n,i}(mNP1):    0.34
 p-value of test no 30                 :    0.90
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     600
 Number of jumps of Y                  :     599
 p-value of test no 31                 :    0.51
 
 Stat. AD (mNP2)                       :    0.28
 p-value of test no 32                 :    0.95
 
 Stat. AD after spacings (mNP2-S)      :    0.24
 p-value of test no 33                 :    0.98
 
 -----------------------------------------------
 CPU time used                    :  00:01:09.69
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.47
 p-value of test no 34                 :    0.77
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    0.78
 p-value of test no 35                 :    0.49
 
 Test on the Nm values of W_{n,i}(mNP1):    0.50
 p-value of test no 36                 :    0.75
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     300
 Number of jumps of Y                  :     283
 p-value of test no 37                 :    0.83
 
 Stat. AD (mNP2)                       :    0.45
 p-value of test no 38                 :    0.80
 
 Stat. AD after spacings (mNP2-S)      :    0.36
 p-value of test no 39                 :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 snpair_ClosePairs test:
 -----------------------------------------------
    N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
 ---------------------------------------
 Test based on the 2 nearest points (NP):
 
 Stat. AD on the N values (NP)         :    0.27
 p-value of test no 40                 :    0.96
 
 
 A2 test based on the spacings between the
    successive jump times of process Y_n(t):
 
 A2 test on the values of A2 (m-NP)    :    1.20
 p-value of test no 41                 :    0.27
 
 Test on the Nm values of W_{n,i}(mNP1):    0.49
 p-value of test no 42                 :    0.76
 
 Test on the jump times of Y
    (superposition of Yn):
 
 Expected number of jumps of Y = mN    :     150
 Number of jumps of Y                  :     157
 p-value of test no 43                 :    0.29
 
 Stat. AD (mNP2)                       :    2.46
 p-value of test no 44                 :    0.05
 
 Stat. AD after spacings (mNP2-S)      :    1.71
 p-value of test no 45                 :    0.13
 
 -----------------------------------------------
 CPU time used                    :  00:02:32.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    6.20
 p-value of test no 46                 :    0.52
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    7
 Chi-square statistic                  :    5.85
 p-value of test no 47                 :    0.56
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   17.60
 p-value of test no 48                 :    0.48
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.75
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_SimpPoker test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   18
 Chi-square statistic                  :   27.90
 p-value of test no 49                 :    0.06
 
 -----------------------------------------------
 CPU time used                    :  00:00:56.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r =  0,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   67.45
 p-value of test no 50                 :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:46.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 10,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   51.57
 p-value of test no 51                 :    0.57
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.32
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 20,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   39.61
 p-value of test no 52                 :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.39
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_CouponCollector test:
 -----------------------------------------------
    N =  1,  n = 200000000,  r = 27,   d =    8
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   54
 Chi-square statistic                  :   54.97
 p-value of test no 53                 :    0.44
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.31
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  232
 Chi-square statistic                  :  212.59
 p-value of test no 54                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:00:44.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
 -----------------------------------------------
 Number of degrees of freedom          :  434
 Chi-square statistic                  :  450.02
 p-value of test no 55                 :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:02:15.10
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 1437
 Chi-square statistic                  : 1453.45
 p-value of test no 56                 :    0.38
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.89
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Gap test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
 -----------------------------------------------
 Number of degrees of freedom          : 7046
 Chi-square statistic                  : 7032.14
 p-value of test no 57                 :    0.54
 
 -----------------------------------------------
 CPU time used                    :  00:02:19.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.073
 p-value of test no 58                 :    0.90
 
 Kolmogorov-Smirnov- statistic = D-    :    0.32
 p-value of test no 59                 :    0.31
 
 Anderson-Darling statistic = A2       :    0.56
 p-value of test no 60                 :    0.68
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   30
 Chi-square statistic                  :   35.51
 p-value of test no 61                 :    0.22
 
 -----------------------------------------------
 CPU time used                    :  00:00:51.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_Run test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.29
 p-value of test no 62                 :    0.16
 
 Kolmogorov-Smirnov- statistic = D-    :    0.11
 p-value of test no 63                 :    0.73
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 64                 :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   60
 Chi-square statistic                  :   50.22
 p-value of test no 65                 :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:02:12.61
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  3,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                  6
        Expected number per cell =  1.6666667e+08
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :    5
 Value of the statistic                :   13.03
 p-value of test no 66                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r =  5,   t =  5,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =                120
        Expected number per cell =   8333333.3
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          :  119
 Value of the statistic                :  104.04
 p-value of test no 67                 :    0.83
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:08.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  5,   t =  7,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =               5040
        Expected number per cell =   99206.349
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 5039
 Value of the statistic                : 4994.74
 p-value of test no 68                 :    0.67
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:05.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_Permutation calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r = 10,   t = 10,
        Sparse =  FALSE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =            3628800
        Expected number per cell =    137.7866
        Hashing =  FALSE
 
    For Delta > -1, we use the ChiSquare approximation
    Correction factor of the ChiSquare: 
        Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
 -----------------------------------------------
 Test Results for Delta =   1.0000
 
 Number of degrees of freedom          : 3628799
 Value of the statistic                : 3.63e+6
 p-value of test no 69                 :    0.71
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:45.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r =  0,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    45830
 p-value of test no 70                 :    0.59
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165869830
   j =  1                              :        399908343
   j =  2                              :            45824
   j =  3                              :                3
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:31.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 Test sknuth_CollisionPermut calling smultin_Multinomial
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smultin_Multinomial test:
 -----------------------------------------------
    N = 20,  n = 20000000,  r = 10,   t = 14,
        Sparse =   TRUE
 
        GenerCell = smultin_GenerCellPermut
        Number of cells = t! =        87178291200
        Expected number per cell =  1 /  4358.9146
        EColl = n^2 / (2k) =   2294.14912
        Hashing =   TRUE
 
        Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
 -----------------------------------------------
 Test Results for Collisions
 
 For the total number of collisions, we use
       the Poisson approximation:
 Expected number of collisions = N*Mu  :    45879.47
 Observed number of collisions         :    46189
 p-value of test no 71                 :    0.07
 
 
 -----------------------------
 Total number of cells containing j balls
 
   j =  0                              :    1743165870189
   j =  1                              :        399907623
   j =  2                              :            46187
   j =  3                              :                1
   j =  4                              :                0
   j =  5                              :                0
 
 -----------------------------------------------
 CPU time used                    :  00:04:35.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.072
 p-value of test no 72                 :    0.63
 
 Kolmogorov-Smirnov- statistic = D-    :   0.098
 p-value of test no 73                 :    0.43
 
 Anderson-Darling statistic = A2       :    0.73
 p-value of test no 74                 :    0.54
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 3999960
 Chi-square statistic                  : 4.00e+6
 p-value of test no 75                 :    0.27
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 76                 :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.044
 p-value of test no 77                 :    0.83
 
 Anderson-Darling statistic = A2       :    2.54
 p-value of test no 78                 :    0.05
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:04.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.017
 p-value of test no 79                 :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 80                 :    0.14
 
 Anderson-Darling statistic = A2       :    1.71
 p-value of test no 81                 :    0.13
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 2999970
 Chi-square statistic                  : 3.00e+6
 p-value of test no 82                 :    0.03
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.056
 p-value of test no 83                 :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 84                 :    0.13
 
 Anderson-Darling statistic = A2       :    0.95
 p-value of test no 85                 :    0.38
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:46.38
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.011
 p-value of test no 86                 :    0.99
 
 Kolmogorov-Smirnov- statistic = D-    :    0.29
 p-value of test no 87                 :    0.03
 
 Anderson-Darling statistic = A2       :    2.87
 p-value of test no 88                 :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 89                 :  9.0e-3
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.23
 p-value of test no 90                 :    0.11
 
 Kolmogorov-Smirnov- statistic = D-    :    0.14
 p-value of test no 91                 :    0.44
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 92                 :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.71
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sknuth_MaxOft test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
       Number of categories = 100000
       Expected number per category  = 100.00
 
 
 -----------------------------------------------
 Test results for chi2 with 99999 degrees of freedom:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.17
 p-value of test no 93                 :    0.30
 
 Kolmogorov-Smirnov- statistic = D-    :   0.086
 p-value of test no 94                 :    0.70
 
 Anderson-Darling statistic = A2       :    0.31
 p-value of test no 95                 :    0.93
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 1999980
 Chi-square statistic                  : 2.00e+6
 p-value of test no 96                 :    0.50
 
 
 -----------------------------------------------
 Test results for Anderson-Darling:
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.051
 p-value of test no 97                 :    0.87
 
 Kolmogorov-Smirnov- statistic = D-    :    0.43
 p-value of test no 98                 :  3.1e-4    *****
 
 Anderson-Darling statistic = A2       :    3.49
 p-value of test no 99                 :    0.02
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:28.07
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 40,  n = 10000000,  r =  0,   t = 8
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.062
 p-value of test no 100                :    0.71
 
 Kolmogorov-Smirnov- statistic = D-    :    0.13
 p-value of test no 101                :    0.25
 
 Anderson-Darling statistic = A2       :    0.91
 p-value of test no 102                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:35.50
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 16
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.068
 p-value of test no 103                :    0.80
 
 Kolmogorov-Smirnov- statistic = D-    :    0.16
 p-value of test no 104                :    0.34
 
 Anderson-Darling statistic = A2       :    0.67
 p-value of test no 105                :    0.59
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.72
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleProd test:
 -----------------------------------------------
    N = 20,  n = 10000000,  r =  0,   t = 24
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.018
 p-value of test no 106                :    0.97
 
 Kolmogorov-Smirnov- statistic = D-    :    0.34
 p-value of test no 107                :  8.2e-3
 
 Anderson-Darling statistic = A2       :    2.45
 p-value of test no 108                :    0.05
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r =  0
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
 p-value of test no 109                :    0.83
 
 Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
 p-value of test no 110                :    0.39
 
 Anderson-Darling statistic = A2       :    0.32
 p-value of test no 111                :    0.92
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.27
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleMean test:
 -----------------------------------------------
    N = 20000000,  n = 30,  r = 10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
 p-value of test no 112                :    0.53
 
 Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
 p-value of test no 113                :    0.71
 
 Anderson-Darling statistic = A2       :    0.38
 p-value of test no 114                :    0.87
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.77
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
 -----------------------------------------------
 Normal statistic                      :    0.56
 p-value of test no 115                :    0.29
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SampleCorr test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
 -----------------------------------------------
 Normal statistic                      :    0.45
 p-value of test no 116                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:00:10.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.24
 p-value of test no 117                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.73
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_AppearanceSpacings test:
 -----------------------------------------------
    N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
    Sequences of n = (K + Q)L =  15150000000 bits
    Q = 10000000 initialization blocks
    K = 1000000000 blocks for the test
    the blocks have L = 15 bits
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.20
 p-value of test no 118                :    0.42
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.26
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   76.89
 p-value of test no 119                :    0.19
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.67
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   59.33
 p-value of test no 120                :    0.74
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.78
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   67
 Chi-square statistic                  :   81.86
 p-value of test no 121                :    0.10
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.85
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   27.18
 p-value of test no 122                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:25.84
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   26.01
 p-value of test no 123                :    0.91
 
 -----------------------------------------------
 CPU time used                    :  00:00:29.03
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_WeightDistrib test:
 -----------------------------------------------
    N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   37
 Chi-square statistic                  :   32.46
 p-value of test no 124                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:28.97
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 svaria_SumCollector test:
 -----------------------------------------------
    N =  1,  n = 500000000,  r =  0,   g = 10
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   29
 Chi-square statistic                  :   49.83
 p-value of test no 125                :  9.4e-3
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.60
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 126                :    0.40
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 127                :    0.50
 
 Anderson-Darling statistic = A2       :    0.50
 p-value of test no 128                :    0.74
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   46.21
 p-value of test no 129                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.25
 p-value of test no 130                :    0.24
 
 Kolmogorov-Smirnov- statistic = D-    :    0.10
 p-value of test no 131                :    0.76
 
 Anderson-Darling statistic = A2       :    0.64
 p-value of test no 132                :    0.60
 
 Test on the sum of all N observations
 Number of degrees of freedom          :   40
 Chi-square statistic                  :   31.18
 p-value of test no 133                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.43
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :   11.40
 p-value of test no 134                :  9.8e-3
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    3
 Chi-square statistic                  :    2.86
 p-value of test no 135                :    0.41
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.11
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    3.68
 p-value of test no 136                :    0.16
 
 -----------------------------------------------
 CPU time used                    :  00:01:10.51
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_MatrixRank test:
 -----------------------------------------------
    N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    2
 Chi-square statistic                  :    2.22
 p-value of test no 137                :    0.33
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.40
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_Savir2 test:
 -----------------------------------------------
    N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.44
 p-value of test no 138                :    0.01
 
 Kolmogorov-Smirnov- statistic = D-    :   0.062
 p-value of test no 139                :    0.89
 
 Anderson-Darling statistic = A2       :    3.07
 p-value of test no 140                :    0.03
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  130
 Chi-square statistic                  :  102.16
 p-value of test no 141                :    0.97
 
 -----------------------------------------------
 CPU time used                    :  00:00:19.90
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 smarsa_GCD test:
 -----------------------------------------------
    N = 10,  n = 50000000,  r =  0,   s = 30
 
 
 -----------------------------------------------
 Test results for GCD values:
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.38
 p-value of test no 142                :    0.04
 
 Kolmogorov-Smirnov- statistic = D-    :   0.081
 p-value of test no 143                :    0.84
 
 Anderson-Darling statistic = A2       :    2.03
 p-value of test no 144                :    0.09
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 17430
 Chi-square statistic                  :17154.14
 p-value of test no 145                :    0.93
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:48.47
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   30.61
 p-value of test no 146                :    0.72
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   31.77
 p-value of test no 147                :    0.63
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   29.96
 p-value of test no 148                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   16.34
 p-value of test no 149                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   17.75
 p-value of test no 150                :    0.41
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:33.68
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :   36
 ChiSquare statistic                   :   40.99
 p-value of test no 151                :    0.26
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :   35
 ChiSquare statistic                   :   29.49
 p-value of test no 152                :    0.73
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :   25
 ChiSquare statistic                   :   42.21
 p-value of test no 153                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :   24
 ChiSquare statistic                   :   39.51
 p-value of test no 154                :    0.02
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   17
 ChiSquare statistic                   :   20.30
 p-value of test no 155                :    0.26
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:34.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  131.44
 p-value of test no 156                :    0.80
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  126.57
 p-value of test no 157                :    0.88
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  487.24
 p-value of test no 158                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  153.93
 p-value of test no 159                :    0.14
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   74.09
 p-value of test no 160                :    0.48
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:38.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  169.88
 p-value of test no 161                :    0.09
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  146
 ChiSquare statistic                   :  147.35
 p-value of test no 162                :    0.45
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          :  500
 ChiSquare statistic                   :  485.27
 p-value of test no 163                :    0.67
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  136
 ChiSquare statistic                   :  107.96
 p-value of test no 164                :    0.96
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :   74
 ChiSquare statistic                   :   85.13
 p-value of test no 165                :    0.18
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:37.82
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  416.84
 p-value of test no 166                :    0.12
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  400.96
 p-value of test no 167                :    0.27
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5073.16
 p-value of test no 168                :    0.23
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  371.92
 p-value of test no 169                :    0.58
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  210.94
 p-value of test no 170                :    0.28
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:31.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 swalk_RandomWalk1 test:
 -----------------------------------------------
    N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
 -----------------------------------------------
 Test on the values of the Statistic H
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  357.51
 p-value of test no 171                :    0.83
 
 
 -----------------------------------------------
 Test on the values of the Statistic M
 
 Number of degrees of freedom          :  384
 ChiSquare statistic                   :  372.76
 p-value of test no 172                :    0.65
 
 
 -----------------------------------------------
 Test on the values of the Statistic J
 
 Number of degrees of freedom          : 5000
 ChiSquare statistic                   : 5081.76
 p-value of test no 173                :    0.21
 
 
 -----------------------------------------------
 Test on the values of the Statistic R
 
 Number of degrees of freedom          :  378
 ChiSquare statistic                   :  404.29
 p-value of test no 174                :    0.17
 
 
 -----------------------------------------------
 Test on the values of the Statistic C
 
 Number of degrees of freedom          :  200
 ChiSquare statistic                   :  195.12
 p-value of test no 175                :    0.58
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:30.88
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   20.14
 p-value of test no 176                :    0.06
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.17
 p-value of test no 177                :    0.57
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.23
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LinearComp test:
 -----------------------------------------------
    N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
 -----------------------------------------------
 Number of degrees of freedom          :   12
 Chi2 statistic for size of jumps      :   17.07
 p-value of test no 178                :    0.15
 
 
 -----------------------------------------------
 Normal statistic for number of jumps  :   -0.90
 p-value of test no 179                :    0.81
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:02:11.65
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.28
 p-value of test no 180                :    0.18
 
 Kolmogorov-Smirnov- statistic = D-    :   0.097
 p-value of test no 181                :    0.78
 
 Anderson-Darling statistic = A2       :    0.47
 p-value of test no 182                :    0.77
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.40
 p-value of test no 183                :    0.65
 
 Sample variance                       :    0.80
 p-value of test no 184                :    0.61
 
 -----------------------------------------------
 CPU time used                    :  00:01:00.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 scomp_LempelZiv test:
 -----------------------------------------------
    N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.14
 p-value of test no 185                :    0.64
 
 Kolmogorov-Smirnov- statistic = D-    :    0.28
 p-value of test no 186                :    0.17
 
 Anderson-Darling statistic = A2       :    0.58
 p-value of test no 187                :    0.67
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.59
 p-value of test no 188                :    0.28
 
 Sample variance                       :    0.77
 p-value of test no 189                :    0.65
 
 -----------------------------------------------
 CPU time used                    :  00:01:02.55
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 190                :    0.31
 
 Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
 p-value of test no 191                :    0.78
 
 Anderson-Darling statistic = A2       :    0.57
 p-value of test no 192                :    0.68
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.93
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sspectral_Fourier3 test:
 -----------------------------------------------
    N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.012
 p-value of test no 193                :    0.32
 
 Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
 p-value of test no 194                :    0.63
 
 Anderson-Darling statistic = A2       :    0.37
 p-value of test no 195                :    0.88
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.35
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    9.12
 p-value of test no 196                :    0.33
 
 -----------------------------------------------
 Global longest run of 1               :   32.00
 p-value of test no 197                :    0.50
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.06
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_LongestHeadRun test:
 -----------------------------------------------
    N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
 -----------------------------------------------
 Number of degrees of freedom          :    8
 Chi-square statistic                  :    5.18
 p-value of test no 198                :    0.74
 
 -----------------------------------------------
 Global longest run of 1               :   36.00
 p-value of test no 199                :    0.07
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:17.02
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r =  0,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.24
 p-value of test no 200                :    0.27
 
 Kolmogorov-Smirnov- statistic = D-    :   0.094
 p-value of test no 201                :    0.79
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 202                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  193.26
 p-value of test no 203                :    0.62
 
 -----------------------------------------------
 CPU time used                    :  00:01:53.96
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_PeriodsInStrings test:
 -----------------------------------------------
    N = 10,  n = 500000000,  r = 20,   s =   10
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.15
 p-value of test no 204                :    0.60
 
 Kolmogorov-Smirnov- statistic = D-    :    0.15
 p-value of test no 205                :    0.59
 
 Anderson-Darling statistic = A2       :    0.36
 p-value of test no 206                :    0.89
 
 Test on the sum of all N observations
 Number of degrees of freedom          :  200
 Chi-square statistic                  :  196.62
 p-value of test no 207                :    0.55
 
 -----------------------------------------------
 CPU time used                    :  00:01:52.13
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.35
 p-value of test no 208                :    0.07
 
 Kolmogorov-Smirnov- statistic = D-    :    0.18
 p-value of test no 209                :    0.47
 
 Anderson-Darling statistic = A2       :    1.96
 p-value of test no 210                :    0.10
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9922.95
 p-value of test no 211                :    0.71
 
 -----------------------------------------------
 CPU time used                    :  00:00:40.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingWeight2 test:
 -----------------------------------------------
    N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.30
 p-value of test no 212                :    0.14
 
 Kolmogorov-Smirnov- statistic = D-    :   0.059
 p-value of test no 213                :    0.90
 
 Anderson-Darling statistic = A2       :    1.04
 p-value of test no 214                :    0.34
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 10000
 Chi-square statistic                  : 9848.58
 p-value of test no 215                :    0.86
 
 -----------------------------------------------
 CPU time used                    :  00:00:41.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
 -----------------------------------------------
 Normal statistic                      :   -0.75
 p-value of test no 216                :    0.77
 
 -----------------------------------------------
 CPU time used                    :  00:00:54.86
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
 -----------------------------------------------
 Normal statistic                      :   0.010
 p-value of test no 217                :    0.50
 
 -----------------------------------------------
 CPU time used                    :  00:00:52.44
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingCorr test:
 -----------------------------------------------
    N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
 -----------------------------------------------
 Normal statistic                      :    0.11
 p-value of test no 218                :    0.46
 
 -----------------------------------------------
 CPU time used                    :  00:03:28.25
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.11
 p-value of test no 219                :    0.72
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 220                :    0.28
 
 Anderson-Darling statistic = A2       :    0.78
 p-value of test no 221                :    0.49
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4974.80
 p-value of test no 222                :    0.20
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.87
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.049
 p-value of test no 223                :    0.92
 
 Kolmogorov-Smirnov- statistic = D-    :    0.20
 p-value of test no 224                :    0.38
 
 Anderson-Darling statistic = A2       :    0.49
 p-value of test no 225                :    0.76
 
 Test on the sum of all N observations
 Number of degrees of freedom          : 4890
 Chi-square statistic                  : 4963.96
 p-value of test no 226                :    0.23
 
 -----------------------------------------------
 CPU time used                    :  00:01:20.22
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 3979.02
 p-value of test no 227                :    0.94
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.17
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 4117
 Chi-square statistic                  : 4176.36
 p-value of test no 228                :    0.26
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.15
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11687.07
 p-value of test no 229                :    0.81
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.46
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_HammingIndep test:
 -----------------------------------------------
    N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
 Counters with expected numbers >= 10
 -----------------------------------------------
 Number of degrees of freedom          : 11825
 Chi-square statistic                  :11672.51
 p-value of test no 230                :    0.84
 
 -----------------------------------------------
 CPU time used                    :  00:01:06.28
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   54.43
 p-value of test no 231                :    0.46
 
 
 -----------------------------------------------
 Total number of bits:  7999786683
 
 Normal statistic for number of bits   :   -1.69
 p-value of test no 232                :    0.95
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:00:58.20
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_Run test:
 -----------------------------------------------
    N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
 -----------------------------------------------
 Total number of 1 runs:  2000000000
 
 Number of degrees of freedom          :   54
 Chi2 statistic for number of runs     :   36.59
 p-value of test no 233                :    0.97
 
 
 -----------------------------------------------
 Total number of bits:  8000065167
 
 Normal statistic for number of bits   :    0.52
 p-value of test no 234                :    0.30
 
 
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.12
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.048
 p-value of test no 235                :    0.93
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 236                :    0.51
 
 Anderson-Darling statistic = A2       :    0.46
 p-value of test no 237                :    0.79
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    0.84
 p-value of test no 238                :    0.20
 
 Sample variance                       :    1.35
 p-value of test no 239                :    0.21
 
 -----------------------------------------------
 CPU time used                    :  00:01:16.70
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :    0.20
 p-value of test no 240                :    0.39
 
 Kolmogorov-Smirnov- statistic = D-    :    0.17
 p-value of test no 241                :    0.50
 
 Anderson-Darling statistic = A2       :    0.55
 p-value of test no 242                :    0.69
 
 Tests on the sum of all N observations
 Standardized normal statistic         :   -0.11
 p-value of test no 243                :    0.54
 
 Sample variance                       :    0.40
 p-value of test no 244                :    0.93
 
 -----------------------------------------------
 CPU time used                    :  00:00:59.81
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.039
 p-value of test no 245                :    0.94
 
 Kolmogorov-Smirnov- statistic = D-    :    0.25
 p-value of test no 246                :    0.24
 
 Anderson-Darling statistic = A2       :    1.49
 p-value of test no 247                :    0.18
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.54
 p-value of test no 248                :    0.06
 
 Sample variance                       :    1.70
 p-value of test no 249                :    0.08
 
 -----------------------------------------------
 CPU time used                    :  00:01:19.05
 
 Generator state:
 
 
 
 
 ***********************************************************
 HOST = n92, Linux
 
 XOshiro256starstar
 
 
 sstring_AutoCor test:
 -----------------------------------------------
    N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
 -----------------------------------------------
 
 Kolmogorov-Smirnov+ statistic = D+    :   0.077
 p-value of test no 250                :    0.85
 
 Kolmogorov-Smirnov- statistic = D-    :    0.24
 p-value of test no 251                :    0.27
 
 Anderson-Darling statistic = A2       :    1.20
 p-value of test no 252                :    0.27
 
 Tests on the sum of all N observations
 Standardized normal statistic         :    1.09
 p-value of test no 253                :    0.14
 
 Sample variance                       :    1.97
 p-value of test no 254                :    0.04
 
 -----------------------------------------------
 CPU time used                    :  00:01:01.61
 
 Generator state:
 
 
 
 
 
 ========= Summary results of BigCrush =========
 
  Version:          TestU01 1.2.3
  Generator:        XOshiro256starstar
  Number of statistics:  160
  Total CPU time:   02:40:47.19
 
  All tests were passed
 
 
 
